NCERT Class 12 Maths
Chapter 7: Integrals
10 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.9
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Evaluate \(\int\limits_{0}^{1} \frac{x}{x^{2} + 1}\, dx\).
Question 2
Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \sqrt{\sin{\left(x \right)}} \cos^{5}{\left(x \right)}\, dx\).
Question 3
Evaluate \(\int\limits_{0}^{1} \operatorname{asin}{\left(\frac{2 x}{x^{2} + 1} \right)}\, dx\).
Question 4
Evaluate \(\int\limits_{0}^{2} x \sqrt{x + 2}\, dx\).
Question 5
Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)} + 1}\, dx\).
Question 6
Evaluate \(\int\limits_{0}^{2} \frac{1}{- x^{2} + x + 4}\, dx\).
Question 7
Evaluate \(\int\limits_{-1}^{1} \frac{1}{x^{2} + 2 x + 5}\, dx\).
Question 8
Evaluate \(\int\limits_{1}^{2} \left(\frac{1}{x} - \frac{1}{2 x^{2}}\right) e^{2 x}\, dx\).
Question 9
Evaluate \(\int\limits_{\frac{1}{3}}^{1} \frac{\sqrt[3]{- x^{3} + x}}{x^{4}}\, dx\).
Question 10
If f(x)=∫₀ˣ t sin t dt, find f′(x).