NCERT Class 12 Maths
Chapter 7: Integrals
39 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.2
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Evaluate \(\int \frac{2 x}{x^{2} + 1}\, dx\).
Question 2
Evaluate \(\int \frac{\log{\left(x \right)}^{2}}{x}\, dx\).
Question 3
Evaluate \(\int \frac{1}{x \log{\left(x \right)} + x}\, dx\).
Question 4
Evaluate \(\int \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}\, dx\).
Question 5
Evaluate \(\int \sin{\left(a x + b \right)} \cos{\left(a x + b \right)}\, dx\).
Question 6
Evaluate \(\int \sqrt{a x + b}\, dx\).
Question 7
Evaluate \(\int x \sqrt{x + 2}\, dx\).
Question 8
Evaluate \(\int x \sqrt{2 x^{2} + 1}\, dx\).
Question 9
Evaluate \(\int \left(4 x + 2\right) \sqrt{x^{2} + x + 1}\, dx\).
Question 10
Evaluate \(\int \frac{1}{- \sqrt{x} + x}\, dx\).
Question 11
Evaluate \(\int \frac{x}{\sqrt{x + 4}}\, dx\).
Question 12
Evaluate \(\int x^{5} \sqrt[3]{x^{3} - 1}\, dx\).
Question 13
Evaluate \(\int \frac{x^{2}}{\left(3 x^{3} + 2\right)^{3}}\, dx\).
Question 14
Evaluate \(\int \frac{\log{\left(x \right)}^{- m}}{x}\, dx\). Here x>0 and m≠1; retain the real-power domain restrictions.
Question 15
Evaluate \(\int \frac{x}{9 - 4 x^{2}}\, dx\).
Question 16
Evaluate \(\int e^{2 x + 3}\, dx\).
Question 17
Evaluate \(\int x e^{- x^{2}}\, dx\).
Question 18
Evaluate \(\int \frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}\, dx\).
Question 19
Evaluate \(\int \frac{e^{2 x} - 1}{e^{2 x} + 1}\, dx\).
Question 20
Evaluate \(\int \frac{e^{2 x} - e^{- 2 x}}{e^{2 x} + e^{- 2 x}}\, dx\).
Question 21
Evaluate \(\int \tan^{2}{\left(2 x - 3 \right)}\, dx\).
Question 22
Evaluate \(\int \sec^{2}{\left(4 x - 7 \right)}\, dx\).
Question 23
Evaluate \(\int \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\, dx\).
Question 24
Evaluate \(\int \frac{- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{4 \sin{\left(x \right)} + 6 \cos{\left(x \right)}}\, dx\).
Question 25
Evaluate \(\int \frac{1}{\left(1 - \tan{\left(x \right)}\right)^{2} \cos^{2}{\left(x \right)}}\, dx\).
Question 26
Evaluate \(\int \frac{\cos{\left(\sqrt{x} \right)}}{\sqrt{x}}\, dx\).
Question 27
Evaluate \(\int \sqrt{\sin{\left(2 x \right)}} \cos{\left(2 x \right)}\, dx\).
Question 28
Evaluate \(\int \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)} + 1}}\, dx\).
Question 29
Evaluate \(\int \log{\left(\sin{\left(x \right)} \right)} \cot{\left(x \right)}\, dx\).
Question 30
Evaluate \(\int \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx\).
Question 31
Evaluate \(\int \frac{\sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}}\, dx\).
Question 32
Evaluate \(\int \frac{1}{\cot{\left(x \right)} + 1}\, dx\).
Question 33
Evaluate \(\int \frac{1}{1 - \tan{\left(x \right)}}\, dx\).
Question 34
Evaluate \(\int \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx\).
Question 35
Evaluate \(\int \frac{\left(\log{\left(x \right)} + 1\right)^{2}}{x}\, dx\).
Question 36
Evaluate \(\int \frac{\left(x + 1\right) \left(x + \log{\left(x \right)}\right)^{2}}{x}\, dx\).
Question 37
Evaluate \(\int \frac{x^{7}}{\left(x^{8} + 1\right)^{\frac{3}{2}}}\, dx\).
Question 38
Evaluate \(\int \frac{10^{x} \log{\left(10 \right)} + 10 x^{9}}{10^{x} + x^{10}}\, dx\).
Question 39
Evaluate \(\int \frac{1}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\, dx\).