These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.10 Questions and Answers are prepared by our highly skilled subject experts. https://mcq-questions.com/ncert-solutions-for-class-12-maths-chapter-7-ex-7-10/
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.10
Question 1.
\(\int_{0}^{1} \frac{x}{x^{2}+1} d x\)
Solution:
Question 2.
\(\int_{0}^{\frac{\pi}{2}} \sqrt{\sin \phi} \cos ^{5} \phi d \phi\)
Solution:
Question 3.
\(\int _{ 0 }^{ 1 }{ { sin }^{ -1 } } \left( \frac { 2x }{ 1+{ x }^{ 2 } } \right) dx\)
Solution:
Question 4.
\(\int_{0}^{2} x \sqrt{x+2}\)
Solution:
Let I = \(\int_{0}^{2} x \sqrt{x+2}\)
let x + 2 = t ∴ dx = dt
when x = 0,t = 2 and when x = 2, t = 4
Question 5.
\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sinx\quad dx }{ 1+{ cos }^{ 2 }x } } \)
Solution:
Question 6.
\(\int _{ 0 }^{ 2 }{ \frac { dx }{ x+4-{ x }^{ 2 } } =I } \)
Solution:
Question 7.
\(\int_{-1}^{1} \frac{d x}{x^{2}+2 x+5}\)
Solution:
Question 8.
\(\int_{1}^{2}\left(\frac{1}{x}-\frac{1}{2 x^{2}}\right) e^{2 x} d x\)
Solution:
Question 9.
The value of the integral \(\int_{\frac{1}{3}}^{1} \frac{\left(x-x^{3}\right)^{\frac{1}{3}}}{x^{4}} d x\) is
(a) 6
(b) 0
(c) 3
(d) 4
Solution:
Question 10.
If \(\int_{0}^{x} t \sin t d t\), then f'(x) is
(a) cosx + xsinx
(b) xsinx
(c) xcosx
(d) sinx+xcosx
Solution:
(b) xsinx
\(f(x)=\int _{ 0 }^{ x }{ tsint\quad dt } \)