{"id":19268,"date":"2022-06-03T12:00:57","date_gmt":"2022-06-03T06:30:57","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=19268"},"modified":"2022-05-21T12:25:40","modified_gmt":"2022-05-21T06:55:40","slug":"mcq-questions-for-class-12-maths-chapter-7","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/","title":{"rendered":"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers"},"content":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers<\/a> during preparation and score maximum marks in the exam. Students can download the Integrals Class 12 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 12 Maths Chapter 7 Integrals Objective Questions.<\/p>\n

Integrals Class 12 MCQs Questions with Answers<\/h2>\n

Students are advised to solve the Integrals Multiple Choice Questions of Class 12 Maths to know different concepts. Practicing the MCQ Questions on Integrals Class 12 with answers will boost your confidence thereby helping you score well in the exam.<\/p>\n

Explore numerous MCQ Questions of Integrals Class 12 with answers provided with detailed solutions by looking below.<\/p>\n

Question 1.
\nThe anti-derivative of (\u221ax + \\(\\frac { 1 }{\u221ax}\\)) equals
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \\(\\frac { 2 }{3}\\) x\\(\\frac { 2 }{3}\\)<\/sup> + 2x\\(\\frac { 1 }{2}\\)<\/sup> + c<\/p>\n<\/details>\n

\n

Question 2.
\nIf \\(\\frac { 1 }{dx}\\) (f(x)) = 4x\u00b3 – \\(\\frac { 3 }{x^4}\\) such that f(2) = 0 then f(x) is ……………
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) x4<\/sup> + \\(\\frac { 1 }{x^3}\\) – \\(\\frac { 129 }{8}\\)<\/p>\n<\/details>\n

\n

Question 3.
\n\u222b\\(\\frac { 10x^9+10^x log_e 10 }{x^{10} + 10^x}\\) dx equals
\n(a) 10x<\/sup> -x10<\/sup> + c
\n(b) 10x<\/sup> + x10<\/sup> + c
\n(c) (10x<\/sup> – x10<\/sup>)-1<\/sup> + c
\n(d) log (10x<\/sup> + x10<\/sup>) + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) log (10x<\/sup> + x10<\/sup>) + c.<\/p>\n<\/details>\n

\n

Question 4.
\n\u222b\\(\\frac { dx }{sin^2 x cos^2 x}\\) equals
\n(a) tan x + cot x + c
\n(b) tan x – cot x + c
\n(c) tan x cot x + c
\n(d) tan x – cot 2x + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) tan x – cot x + c<\/p>\n<\/details>\n

\n

Question 5.
\n\u222b\\(\\frac { sin^2 x – cos ^2 x }{sin^2 x cos^2 x}\\) dx is equals to
\n(a) tan x + cot x + c
\n(b) tan x + cosec x + c
\n(c) -tan x + cot x + c
\n(d) tan x + sec x + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) tan x + cot x + c<\/p>\n<\/details>\n

\n

Question 6.
\n\u222b\\(\\frac { e^x(1 + x) }{cos^2(xe^2)}\\) dx is equals to
\n(a) -cot (xex<\/sup>) + c
\n(b) tan (xex<\/sup>) + c
\n(c) tan (ex<\/sup>) + c
\n(d) cot (ex<\/sup>) + c<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) tan (xex<\/sup>) + c<\/p>\n<\/details>\n

\n

Question 7.
\n\u222b\\(\\frac { dx }{x^2+2x+2}\\) equals
\n(a) x tan-1<\/sup> (x + 1) + c
\n(b) tan-1<\/sup> (x + 1) + c
\n(c) (x + 1) tan-1<\/sup> x + c
\n(d) tan-1<\/sup> x + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) tan-1<\/sup> (x + 1) + c<\/p>\n<\/details>\n

\n

Question 8.
\n\u222b\\(\\frac { dx }{\\sqrt{9-25x^2}}\\) equals
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) \\(\\frac { 1 }{5}\\) sin-1<\/sup> (\\(\\frac { 5x }{3}\\)) + c<\/p>\n<\/details>\n

\n

Question 9.
\n\u222b\\(\\frac { x dx }{(x-1)(x-2)}\\) equals
\n\"MCQ
\n(d) log |(x – 1) (x – 2)| + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) log |\\(\\frac { (x-2)^2 }{x-1}\\)| + c<\/p>\n<\/details>\n

\n

Question 10.
\n\u222b\\(\\frac { dx }{x(x^2+1)}\\) equals
\n(a) log |x| – \\(\\frac { 1 }{2}\\) log (x\u00b2 + 1) + c
\n(b) \\(\\frac { 1 }{2}\\) log |x| + \\(\\frac { 1 }{2}\\) log (x\u00b2 + 1) + c
\n(c) -log |x| + \\(\\frac { 1 }{2}\\) log (x\u00b2 + 1) + c
\n(d) log |x| + log (x\u00b2 + 1) + c<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) log |x| – \\(\\frac { 1 }{2}\\) log (x\u00b2 + 1) + c<\/p>\n<\/details>\n

\n

Question 11.
\n\u222bx\u00b2 ex\u00b3<\/sup> dx equals
\n(a) \\(\\frac { 1 }{3}\\) ex\u00b3<\/sup> + c
\n(b) \\(\\frac { 1 }{3}\\) ex\u00b2<\/sup> + c
\n(c) \\(\\frac { 1 }{2}\\) ex\u00b3<\/sup> + c
\n(d) \\(\\frac { 1 }{2}\\) ex\u00b2<\/sup> + c<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) \\(\\frac { 1 }{3}\\) ex\u00b3<\/sup> + c<\/p>\n<\/details>\n

\n

Question 12.
\n\u222bex<\/sup> sec x (1 + tan x) dx equals
\n(a) ex<\/sup> cos x + c
\n(b) ex<\/sup> sec x + c
\n(c) ex<\/sup> sin x + c
\n(d) ex<\/sup> tan x + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) ex<\/sup> sec x + c<\/p>\n<\/details>\n

\n

Question 13.
\n\u222b\\(\\sqrt { 1 + x^2}\\) dx is equal to
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer:
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 14.
\n\u222b\\(\\sqrt { x^2 – 8x + 7}\\) dx is equal to
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer:
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 15.
\n\\(\\int_{1}^{\\sqrt{3}}\\) \\(\\frac { dx }{1+x^2}\\) equals
\n(a) \\(\\frac { \u03c0 }{3}\\)
\n(b) \\(\\frac { 2\u03c0 }{3}\\)
\n(c) \\(\\frac { \u03c0 }{6}\\)
\n(d) \\(\\frac { \u03c0 }{112}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) \\(\\frac { \u03c0 }{112}\\)<\/p>\n<\/details>\n

\n

Question 16.
\n\\(\\int_{1}^{2\/3}\\) \\(\\frac { dx }{4+9x^2}\\) equals
\n(a) \\(\\frac { \u03c0 }{6}\\)
\n(b) \\(\\frac { \u03c0 }{12}\\)
\n(c) \\(\\frac { \u03c0 }{24}\\)
\n(d) \\(\\frac { \u03c0 }{4}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \\(\\frac { \u03c0 }{24}\\)<\/p>\n<\/details>\n

\n

Question 17.
\nThe value of the integral \\(\\int_{1}^{2\/3}\\) \\(\\frac { (x-x^3)^{1\/3} }{x^4}\\) dx is
\n(a) 6
\n(b) 0
\n(c) 3
\n(d) 4<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 6<\/p>\n<\/details>\n

\n

Question 18.
\nIf f(x) = \\(\\int_{0}^{x}\\) t sin t dt, then f'(x) is
\n(a) cos x + x sin x
\n(b) x sin x
\n(c) x cos x
\n(d) sin x + x cos x.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) x sin x<\/p>\n<\/details>\n

\n

Question 19.
\nThe value of
\n\\(\\int_{-\u03c0\/2}^{\u03c0\/2}\\) (x\u00b3 + x cos x + tan5<\/sup> x + 1) dx is
\n(a) 0
\n(b) 2
\n(c) \u03c0
\n(d) 1<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \u03c0<\/p>\n<\/details>\n

\n

Question 20.
\nThe value of \\(\\int_{0}^{\u03c0\/2}\\) log (\\(\\frac { 4+3 sin x }{4+3 cos x}\\)) dx is
\n(a) 2
\n(b) \\(\\frac { 3 }{4}\\)
\n(c) 0
\n(d) -2<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 0<\/p>\n<\/details>\n

\n

Question 21.
\n\u222b\\(\\frac { dx }{e^x+e{-x}}\\) is equal to
\n(a) tan-1<\/sup> (ex<\/sup>) + c
\n(b) tan-1<\/sup> (e-x<\/sup>) + c
\n(c) log (ex<\/sup> – e-1<\/sup>) + c
\n(d) log (ex<\/sup> + e-x<\/sup>) + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) tan-1<\/sup> (ex<\/sup>) + c<\/p>\n<\/details>\n

\n

Question 22.
\n\u222b\\(\\frac { cos 2x }{(sin x + cos x)^2}\\) dx is equal to
\n(a) \\(\\frac { -1 }{sin x + cos x}\\) + c
\n(b) log |sin x + cos x| + c
\n(c) log |sin x – cos x| + c
\n(d) \\(\\frac { 1 }{(sin x + cos x)^2}\\) + c<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) log |sin x + cos x| + c<\/p>\n<\/details>\n

\n

Question 23.
\nIf f (a + b – x) = f(x), then \\(\\int_{a}^{b}\\) x f(x) dx is equal to
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) \\(\\frac { a+b }{2}\\) \\(\\int_{a}^{b}\\) f(x) dx<\/p>\n<\/details>\n

\n

Question 24.
\n\u222bex<\/sup>(cos x – sin x)dx is equal to
\n(a) ex<\/sup> – cos x + c
\n(b) ex<\/sup> sin x + c
\n(c) -ex<\/sup> cos x + c
\n(d) -ex<\/sup> sin x + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) ex<\/sup> – cos x + c<\/p>\n<\/details>\n

\n

Question 25.
\n\u222b\\(\\frac { dx }{sin^2 x cos^2 x}\\) is equal to
\n(a) tan x + cot x + c
\n(b) (tan x + cot x)\u00b2 + c
\n(c) tan x – cot x + c
\n(d) (tan x – cot x)\u00b2 + c.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) tan x – cot x + c<\/p>\n<\/details>\n

\n

Question 26.
\nIf \u222b \\(\\frac { 3e^x-5e^{-x} }{4r^x+5e^{-x}}\\) dx = ax + b log |4ex<\/sup> + 5e-x<\/sup>| + c then
\n(a) a = –\\(\\frac { 1 }{8}\\), b = \\(\\frac { 7 }{8}\\)
\n(b) a = \\(\\frac { 1 }{8}\\), b = \\(\\frac { 7 }{8}\\)
\n(c) a = \\(\\frac { -1 }{8}\\), b = –\\(\\frac { 7 }{8}\\)
\n(d) a = \\(\\frac { 1 }{8}\\), b = –\\(\\frac { 7 }{8\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) a = –\\(\\frac { 1 }{8}\\), b = \\(\\frac { 7 }{8}\\)<\/p>\n<\/details>\n

\n

Question 27.
\n\u222btan-1<\/sup> \u221ax dx is equal to
\n(a) (x + 1)tan-1<\/sup> \u221ax – \u221ax + c
\n(b) x tan-1<\/sup> \u221ax – \u221ax + c
\n(c) \u221ax – x tan-1<\/sup> \u221ax + c
\n(d) -1<\/sup>x – (x + 1) tan-1<\/sup> \u221ax + c<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) (x + 1)tan-1<\/sup> \u221ax – \u221ax + c<\/p>\n<\/details>\n

\n

Question 28.
\n\u222bex<\/sup>(\\(\\frac { 1-x }{(1+x^2)}\\))2<\/sup> dx is equal to:
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \\(\\frac { e^x }{(1+x^2)^2}\\) + c<\/p>\n<\/details>\n

\n

Question 29.
\n\\(\\int_{a+c}^{b+c}\\) f(x)dx is equal to :
\n(a) \\(\\int_{c}^{b}\\) f(x – c)dx
\n(b) \\(\\int_{c}^{b}\\) f(x + c)dx
\n(c) \\(\\int_{c}^{b}\\) f(x)dx
\n(d) \\(\\int_{a-c}^{b-c}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) \\(\\int_{c}^{b}\\) f(x + c)dx<\/p>\n<\/details>\n

\n

Question 30.
\n\\(\\int_{-1}^{1}\\) \\(\\frac { x^3+|x|+1 }{x^2+2|x|+1}\\) is equal to
\n(a) log 2
\n(b) 2 log 2
\n(c) \\(\\frac { 1 }{2}\\) log 2
\n(d) 4 log 2<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 2 log 2<\/p>\n<\/details>\n

\n

Question 31.
\n\\(\\int_{c}^{b}\\) |x cos \u03c0x|dx is equal to
\n(a) \\(\\frac { 8 }{\u03c0}\\)
\n(b) \\(\\frac { 4 }{\u03c0}\\)
\n(c) \\(\\frac { 2 }{\u03c0}\\)
\n(d) \\(\\frac { 1 }{\u03c0}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) \\(\\frac { 8 }{\u03c0}\\)<\/p>\n<\/details>\n

\n

Question 32.
\nIf \\(\\int_{0}^{1}\\) \\(\\frac { e^t }{1+t}\\) dt = a, then \\(\\int_{0}^{1}\\) \\(\\frac { e^t }{(1+t)^2}\\)
\n(a) a – 1 + \\(\\frac { e }{2}\\)
\n(b) a + 1 – \\(\\frac { e }{2}\\)
\n(c) a – 1 – \\(\\frac { e }{2}\\)
\n(d) a + 1 + \\(\\frac { e }{2}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) a + 1 – \\(\\frac { e }{2}\\)<\/p>\n<\/details>\n

\n

Question 33.
\nIf x = \\(\\int_{0}^{y}\\) \\(\\frac { dt }{\\sqrt{1+9t^2}}\\) and \\(\\frac { d^y }{dx^2}\\) = ay, then a is equal to
\n(a) 3
\n(b) 6
\n(c) 9
\n(d) 1.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 9<\/p>\n<\/details>\n

\n

Question 34.
\nLet I = \\(\\int_{0}^{1}\\) \\(\\frac { sin x }{\u221ax}\\) dx and J = \\(\\int_{0}^{1}\\) \\(\\frac { cos x }{\u221ax}\\) dx. Then which of the following is true?
\n(a) I > \\(\\frac { 2 }{3}\\) and J < 2
\n(b) I > \\(\\frac { 2 }{3}\\) and J > 2
\n(c) I < \\(\\frac { 2 }{3}\\) and J < 2
\n(d) I < \\(\\frac { 2 }{3}\\) and J > 2.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) I < \\(\\frac { 2 }{3}\\) and J < 2
\nHint:
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 35.
\n\\(\\int_{0}^{\u03c0}\\) [cot x]dx, where [ . ] denotes the greatest integer function, is equal to
\n(a) \\(\\frac { \u03c0 }{2}\\)
\n(b) 2
\n(c) -1
\n(d) –\\(\\frac { \u03c0 }{2}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) –\\(\\frac { \u03c0 }{2}\\)
\nHint:
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 36.
\nLet p (x) be a function defined on R such that p'(x) = p'(1 – x), for all x \u2208 [0, 1], p(0) = 1 and p (1) = 41.
\nThen \\(\\int_{0}^{1}\\) p(x) dx equals
\n(a) \\(\\sqrt { 41}\\)
\n(b) 21
\n(c) 41
\n(d) 42<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 21
\nHint:
\nHere p'(x) – p'(1 – x).
\nIntegrating, p (x) = -p (1 – x) + c ………… (1)
\nAt x = 0, p(0) = -p (1) + c
\n\u21d2 1 = -41 + c \u21d2 c = 42.
\nPutting in (1),
\np (x) = -p(1 – x) + 42
\n\u2234 \\(\\int_{0}^{1}\\) p(x) dx = –\\(\\int_{0}^{1}\\) p(1 – x)dx + \\(\\int_{0}^{1}\\) 42 dx
\n\u21d2 21 = 42[x]\\(_{ 0 }^{1}\\)
\n\u21d2 21 = 42
\n\u21d2 I = 21.<\/p>\n<\/details>\n

\n

Question 37.
\nLet In<\/sub> = \u222btan” x dx, (n > 1).
\nIf I4<\/sub> + I6<\/sub> = a tan5<\/sup> x + bx5<\/sup> + c, where c is a constant of integration, then the ordered pair (a, b) is equal to
\n(a) (\\(\\frac { 1}{5}\\), -1)
\n(b) (-\\(\\frac { 1}{5}\\), 0)
\n(c) (-\\(\\frac { 1}{5}\\), 1)
\n(d) (\\(\\frac { 1}{5}\\), 0)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) (\\(\\frac { 1}{5}\\), 0)
\nHint:
\nHere I4<\/sub> + I6<\/sub> = a tan5<\/sup> x + bx5<\/sup> + c
\n\u21d2 \u222btan4<\/sup>x dx + \u222btan6<\/sup> x dx = a tan5<\/sup> x + bx5<\/sup> + c.
\nDiff. both sides,
\ntan4<\/sup> x + tan6<\/sup> x = 5a tan4<\/sup> x sec\u00b2 x + 5bx4<\/sup>
\n= 5 a tan4<\/sup> x(1 + tan2<\/sup> x) + 5 bx4<\/sup>
\n= 5a tan4<\/sup> x + 5a tan6<\/sup>x + 5bx4<\/sup>.
\nComparing, 1 = 5a and 5b = 0
\n\u21d2 a = \\(\\frac { 1 }{5}\\) and b = 0.
\nHence, (a, b) = (\\(\\frac { 1}{5}\\), 0)<\/p>\n<\/details>\n

\n

Question 38.
\nThe integral
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) \\(\\frac {-1}{3(1+tan^3 x)}\\) + c
\nHint:
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 39.
\nThe value of \\(\\int_{-\u03c0\/2}^{\u03c0\/2}\\) \\(\\frac { sin^2 x }{1 + 2^x}\\) dx is
\n(a) \\(\\frac { \u03c0}{8}\\)
\n(b) \\(\\frac {\u03c0}{2}\\)
\n(c) 4\u03c0
\n(d) \\(\\frac {\u03c0}{4}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) \\(\\frac {\u03c0}{4}\\)
\nHint:
\n\"MCQ<\/p>\n<\/details>\n

\n

Fill in the blanks<\/span><\/p>\n

Question 1.
\n\u222b(\u221ax + \\(\\frac {1}{\u221ax}\\)) dx (x \u2260 0) = ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 2 }{3}\\) x\u221ax + 2\u221ax<\/p>\n<\/details>\n

\n

Question 2.
\n\u222bcot x dx = ………………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: log |sin x| + c<\/p>\n<\/details>\n

\n

Question 3.
\n\u222bsec x dx = ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: log |sec x + tan x| + c<\/p>\n<\/details>\n

\n

Question 4.
\n\u222b \\(\\frac { sin^2 x – cos^2 x }{sin x cos x}\\) dx = ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: log |sec x| – log |sin x| + c<\/p>\n<\/details>\n

\n

Question 5.
\n\u222b \\(\\frac { x^3+5x^2+4 }{x^2}\\) dx = ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { x^2 }{2}\\) + 5x – \\(\\frac { 4 }{x}\\) + c<\/p>\n<\/details>\n

\n

Question 6.
\n\u222btan\u00b2 x dx ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: tan x – x+ c<\/p>\n<\/details>\n

\n

Question 7.
\n\u222b \\(\\sqrt { a^2+x^2}\\) dx = ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac{x \\sqrt{a^{2}+x^{2}}}{2}\\) + \\(\\frac { a^2 }{2}\\) log|x + \\(\\sqrt { a^2+x^2}\\)| + c<\/p>\n<\/details>\n

\n

Question 8.
\n\u222b (2 – x) sin x dx = ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: -2 cos x + x cos x – sin x + c<\/p>\n<\/details>\n

\n

Question 9.
\nIf \u222b ex<\/sup>(tan x + 1) sec x dx = ex<\/sup> f(x) + c, then f(x) = ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: sec x<\/p>\n<\/details>\n

\n

Question 10.
\n\u222b \\(\\frac { 1 }{9x^2-1}\\) dx = …………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 1 }{6}\\) log |\\(\\frac { 3x-1 }{3x+1}\\)| + c<\/p>\n<\/details>\n

\n

Question 11.
\n\\(\\int_{2}^{3}\\) 3x<\/sup> dx = …………………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 18 }{log 3}\\)<\/p>\n<\/details>\n

\n

Question 12.
\n\\(\\int_{0}^{1}\\) \\(\\frac { dx }{\\sqrt{1+x^2}}\\) = ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: log (1 + \u221a2)<\/p>\n<\/details>\n

\n

Question 13.
\nIf \\(\\int_{0}^{1}\\) (3x\u00b2 + 2x + k) dx = 0, then the value of ‘k’ ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: -2<\/p>\n<\/details>\n

\n

Question 14.
\nIf f(x) = \\(\\int_{0}^{x}\\) t sin t dt, then the value of f'(x) = ………………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: x sin x<\/p>\n<\/details>\n

\n

Question 15.
\n\\(\\int_{0}^{1.5}\\) [x] dx = ………………. where [x] is greatest integer function.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 0.5<\/p>\n<\/details>\n

\n

We believe the knowledge shared regarding NCERT MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Pdf free download has been useful to the possible extent. If you have any other queries regarding CBSE Class 12 Maths Integrals MCQs Multiple Choice Questions with Answers, feel free to reach us via the comment section and we will guide you with the possible solution.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. Students can download …<\/p>\n

MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[35],"tags":[],"yoast_head":"\nMCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. Students can download … MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ Questions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-06-03T06:30:57+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-05-21T06:55:40+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/02\/MCQ-Questions-for-Class-12-Maths-Chapter-7-Integrals-with-Answers-1.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mcq-questions.com\/#website\",\"url\":\"https:\/\/mcq-questions.com\/\",\"name\":\"MCQ Questions\",\"description\":\"MCQ Questions for Class 1 to 12\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mcq-questions.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i1.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/02\/MCQ-Questions-for-Class-12-Maths-Chapter-7-Integrals-with-Answers-1.png?fit=165%2C234&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/02\/MCQ-Questions-for-Class-12-Maths-Chapter-7-Integrals-with-Answers-1.png?fit=165%2C234&ssl=1\",\"width\":165,\"height\":234,\"caption\":\"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#webpage\",\"url\":\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/\",\"name\":\"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers - MCQ Questions\",\"isPartOf\":{\"@id\":\"https:\/\/mcq-questions.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#primaryimage\"},\"datePublished\":\"2022-06-03T06:30:57+00:00\",\"dateModified\":\"2022-05-21T06:55:40+00:00\",\"author\":{\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\"},\"breadcrumb\":{\"@id\":\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mcq-questions.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/mcq-questions.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers - MCQ Questions","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/","og_locale":"en_US","og_type":"article","og_title":"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers - MCQ Questions","og_description":"Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. Students can download … MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Read More »","og_url":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2022-06-03T06:30:57+00:00","article_modified_time":"2022-05-21T06:55:40+00:00","og_image":[{"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/02\/MCQ-Questions-for-Class-12-Maths-Chapter-7-Integrals-with-Answers-1.png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"10 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i1.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/02\/MCQ-Questions-for-Class-12-Maths-Chapter-7-Integrals-with-Answers-1.png?fit=165%2C234&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/02\/MCQ-Questions-for-Class-12-Maths-Chapter-7-Integrals-with-Answers-1.png?fit=165%2C234&ssl=1","width":165,"height":234,"caption":"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers 1"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#webpage","url":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/","name":"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers - MCQ Questions","isPartOf":{"@id":"https:\/\/mcq-questions.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#primaryimage"},"datePublished":"2022-06-03T06:30:57+00:00","dateModified":"2022-05-21T06:55:40+00:00","author":{"@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3"},"breadcrumb":{"@id":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-7\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mcq-questions.com\/"},{"@type":"ListItem","position":2,"name":"MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers"}]},{"@type":"Person","@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/mcq-questions.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/19268"}],"collection":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/comments?post=19268"}],"version-history":[{"count":1,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/19268\/revisions"}],"predecessor-version":[{"id":34564,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/19268\/revisions\/34564"}],"wp:attachment":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/media?parent=19268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/categories?post=19268"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/tags?post=19268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}