Class 12 Maths Ex7.2 Question 1.<\/strong> \n\\(\\frac { 2x }{ 1+{ x }^{ 2 } }\\) \nSolution: \nLet 1 + x\u00b2 = t \n\u21d2 2xdx = dt \n\u2234 \u222b\\(\\frac { 2x }{ 1+{ x }^{ 2 } }\\) dx \n= \u222b\\(\\frac { dt }{ t }\\) \n= log t + C \n= log(1 + x\u00b2) + C<\/p>\nQuestion 2. \n\\(\\frac { { \\left( logx \\right) }^{ 2 } }{ x } \\) \nSolution: \nLet logx = t \n\u21d2 \\(\\frac { 1 }{ x }dx=dt\\) \n\\(\\int \\frac{(\\log x)^{2}}{x} d x=\\int t^{2} d t=\\frac{t^{3}}{3}+\\mathrm{C}\\) \n= \\(\\frac{1}{3}(\\log x)^{3}+\\mathrm{C}\\)<\/p>\n
Question 3. \n\\(\\frac { 1 }{ x+xlogx }\\) \nSolution: \nPut 1 + logx = t \n\u2234 \\(\\frac { 1 }{ x }\\)dx = dt \n\\(\\int { \\frac { 1 }{ x(1+logx) } dx } =\\int { \\frac { 1 }{ t } dt } =log|t| + C \\) \n= log|1+logx| + C<\/p>\n
<\/p>\n
Question 4. \nsinx sin(cosx) \nSolution: \n\u222bsinx sin(cosx)dx = \u222bsin t dt \n= – (-cos t) + C \n= – cost + C \n= cos(cos x) + C<\/p>\n
Question 5. \nsin(ax+b) cos(ax+b) \nSolution: \n \nAnother method: \n <\/p>\n
Question 6. \n\\(\\sqrt { ax+b }\\) \nSolution: \n <\/p>\n
Question 7. \nx\\(\\sqrt { x+2 }\\) \nSolution: \n <\/p>\n
Question 8. \nx\\(\\sqrt { 1+{ 2x }^{ 2 } }\\) \nSolution: \n <\/p>\n
Question 9. \n(4x+2)\\(\\sqrt { { x }^{ 2 }+ x + 1 } \\) \nSolution: \n <\/p>\n
<\/p>\n
Question 10. \n\\(\\frac { 1 }{ x-\\sqrt { x } } \\) \nSolution: \n <\/p>\n
Question 11. \n\\(\\frac { x }{ \\sqrt { x+4 } }\\) , x > 0 \nSolution: \n <\/p>\n
Question 12. \n\\({ { (x }^{ 3 }-1) }^{ \\frac { 1 }{ 3 } }.{ x }^{ 5 }\\) \nSolution: \n <\/p>\n
Question 13. \n\\(\\frac { { x }^{ 2 } }{ { { (2+3x }^{ 3 }) }^{ 3 } } \\) \nSolution: \n <\/p>\n
Question 14. \n\\(\\frac { 1 }{ x(logx)^{ m } }\\), x > 0 \nSolution: \nPut log x = t, \\(\\frac { dt }{ dx }\\) = \\(\\frac { 1 }{ x }\\) \u21d2 dt = \\(\\frac { 1 }{ x }\\)dx \n\\(\\int \\frac{1}{x(\\log x)^{m}} d x=\\int \\frac{d t}{t^{m}}=\\int t^{-m} d t=\\frac{t^{-m+1}}{-m+1}+\\mathrm{C}\\) \n\\(=\\frac { { (logx) }^{ 1-m } }{ 1-m }\\) + C<\/p>\n
<\/p>\n
Question 15. \n\\(\\frac { x }{ 9-4{ x }^{ 2 } } \\) \nSolution: \n <\/p>\n
Question 16. \n\\({ e }^{ 2x+3 }\\) \nSolution: \nput 2x + 3 = t \nso that 2dx = dt \n\\(\\int { { e }^{ 2x+3 } } dx\\quad =\\frac { 1 }{ 2 } \\int { { e }^{ t }dt } \\quad =\\frac { 1 }{ 2 } { e }^{ t }+c\\quad =\\frac { 1 }{ 2 } { e }^{ 2x+3 }\\) + C<\/p>\n
Question 17. \n\\(\\frac { x }{ { e }^{ { x }^{ 2 } } } \\) \nSolution: \n <\/p>\n
Question 18. \n\\(\\frac { { e }^{ { tan }^{ -1 }x } }{ 1+{ x }^{ 2 } } \\) \nSolution: \nlet \\(\\quad { tan }^{ -1 }x=t\\Rightarrow \\frac { 1 }{ 1+{ x }^{ 2 } } dx=dt\\) \n\u2234 \\(\\frac { { e }^{ { tan }^{ -1 }x } }{ 1+{ x }^{ 2 } } \\)dx \n= \u222bet<\/sup> dt \n= et<\/sup>+C \n= etan-1 <\/sup>+ C<\/p>\nQuestion 19. \n\\(\\frac { { e }^{ 2x }-1 }{ { e }^{ 2x }+1 } \\) \nSolution: \n \nAnother method \n <\/p>\n
Question 20. \n\\(\\frac { { e }^{ 2x }-{ e }^{ 2x } }{ { e }^{ 2x }+{ e }^{ -2x } } \\) \nSolution: \n <\/p>\n
Question 21. \ntan\u00b2(2x – 3) \nSolution: \n\u222btan\u00b2(2x – 3)dx = \u222b[sec\u00b2(2x – 3) – 1]dx = I \nput 2x – 3 = t \nso that 2dx = dt \nI = \\(\\frac { 1 }{ 2 }\\) \u222bsec\u00b2t dt – x + C \n= \\(\\frac { 1 }{ 2 }\\)t – x + C \n= \\(\\frac { 1 }{ 2 }\\)tan(2x -3 ) – x + C<\/p>\n
<\/p>\n
Question 22. \nsec\u00b2(7 – 4x) \nSolution: \n\u222bsec\u00b2(7 – 4x)dx \n= \\(\\frac { tan(7-4x) }{ -4 }\\) + C<\/p>\n
Question 23. \n\\(\\frac { { sin }^{ -1 }x }{ \\sqrt { 1-{ x }^{ 2 } } } \\) \nSolution: \nLet \\(\\quad { sin }^{ -1 }x=t\\quad\\Rightarrow\\frac { 1dx }{ \\sqrt { 1-{ x }^{ 2 } } }\\) = dt \n\\(\\int { \\frac { { sin }^{ -1 }x }{ \\sqrt { 1-{ x }^{ 2 } } } dx } =\\int { t\\quad dt } =\\frac { 1 }{ 2 } { t }^{ 2 }+c=\\frac { 1 }{ 2 } { { (sin }^{ -1 }x) }^{ 2 }+c\\)<\/p>\n
Question 24. \n\\(\\frac { 2cosx-3sinx }{ 6cosx+4sinx }\\) \nSolution: \n <\/p>\n
Question 25. \n\\(\\frac { 1 }{ { cos }^{ 2 }x{ (1-tanx) }^{ 2 } } \\) \nSolution: \n <\/p>\n
<\/p>\n
Question 26. \n\\(\\frac { cos\\sqrt { x } }{ \\sqrt { x } } \\) \nSolution: \n <\/p>\n
Question 27. \n\\(\\sqrt { sin2x } cos2x\\) \nSolution: \n <\/p>\n
Question 28. \n\\(\\frac { cosx }{ \\sqrt { 1+sinx } } \\) \nSolution: \n <\/p>\n
Question 29. \ncotx log sinx \nSolution: \n <\/p>\n
Question 30. \n\\(\\frac { sinx }{ 1+cosx }\\) \nSolution: \nput 1 + cosx = t \n\u21d2 – sinx dx = dt \n\u222b\\(\\frac { sinx }{ 1+cosx }\\)dx \n= – \\(\\frac { dt }{ t }\\) \n= – log|t| + c \n= – log|1 + cosx| + C \n= \\(\\log \\left|\\frac{1}{1+\\cos x}\\right|+\\mathrm{C}\\)<\/p>\n
<\/p>\n
Question 31. \n\\(\\frac { sinx }{ { (1+cosx) }^{ 2 } } \\) \nSolution: \nput 1 + cosx = t \nso that – sinx dx = dt \n\u222b\\(\\frac { sinx }{ { (1+cosx) }^{ 2 } } \\) = – \\(\\int \\frac{d t}{t^{2}}=\\frac{1}{t}+C\\) \n= \\(\\frac { 1 }{ t }\\) + C \n= \\(\\frac { 1 }{ 1 + cosx }\\) + C<\/p>\n
Question 32. \n\\(\\frac { 1 }{ 1 + cotx }\\) \nSolution: \n <\/p>\n
Question 33. \n\\(\\frac { 1 }{ 1-tanx }\\) \nSolution: \n <\/p>\n
Question 34. \n\\(\\frac { \\sqrt { tanx } }{ sinxcosx } \\) \nSolution: \n <\/p>\n
Question 35. \n\\(\\frac { { (1+logx) }^{ 2 } }{ x } \\) \nSolution: \n <\/p>\n
Question 36. \n\\(\\frac { (x+1){ (x+logx) }^{ 2 } }{ x } \\) \nSolution: \n <\/p>\n
<\/p>\n
Question 37. \n\\(\\frac { { x }^{ 3 }sin({ tan }^{ -1 }{ x }^{ 4 }) }{ 1+{ x }^{ 8 } } dx \\) \nSolution: \n <\/p>\n
Question 38. \n\\(\\int { \\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>) + C \n(d) log (10x<\/sup> + x10<\/sup>) + C \nSolution: \n(d) log (10x<\/sup> + x10<\/sup>) + C \n <\/p>\nQuestion 39. \n\\(\\int { \\frac { dx }{ { sin }^{ 2 }x{ \\quad cos }^{ 2 }x } = } \\) \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 2 x + c \nSolution: \n(b) tan x – cot x + c \n <\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-2\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.2 Class 12 Maths Ex7.2 Question 1. Solution: Let 1 + x\u00b2 = t \u21d2 2xdx = dt \u2234 \u222b dx …<\/p>\n
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2<\/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":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n