NCERT Class 12 Maths
Chapter 7: Integrals
24 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.3
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Evaluate \(\int \sin^{2}{\left(2 x + 5 \right)}\, dx\).
Question 2
Evaluate \(\int \sin{\left(3 x \right)} \cos{\left(4 x \right)}\, dx\).
Question 3
Evaluate \(\int \cos{\left(2 x \right)} \cos{\left(4 x \right)} \cos{\left(6 x \right)}\, dx\).
Question 4
Evaluate \(\int \sin^{3}{\left(2 x + 1 \right)}\, dx\).
Question 5
Evaluate \(\int \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}\, dx\).
Question 6
Evaluate \(\int \sin{\left(x \right)} \sin{\left(2 x \right)} \sin{\left(3 x \right)}\, dx\).
Question 7
Evaluate \(\int \sin{\left(4 x \right)} \sin{\left(8 x \right)}\, dx\).
Question 8
Evaluate \(\int \frac{1 - \cos{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx\).
Question 9
Evaluate \(\int \frac{\cos{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx\).
Question 10
Evaluate \(\int \sin^{4}{\left(x \right)}\, dx\).
Question 11
Evaluate \(\int \cos^{4}{\left(2 x \right)}\, dx\).
Question 12
Evaluate \(\int \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx\).
Question 13
Evaluate \(\int \frac{- \cos{\left(2 \alpha \right)} + \cos{\left(2 x \right)}}{- \cos{\left(\alpha \right)} + \cos{\left(x…
Question 14
Evaluate \(\int \frac{- \sin{\left(x \right)} + \cos{\left(x \right)}}{\sin{\left(2 x \right)} + 1}\, dx\).
Question 15
Evaluate \(\int \tan^{3}{\left(2 x \right)} \sec{\left(2 x \right)}\, dx\).
Question 16
Evaluate \(\int \tan^{4}{\left(x \right)}\, dx\).
Question 17
Evaluate \(\int \frac{\sin^{3}{\left(x \right)} + \cos^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\…
Question 18
Evaluate \(\int \frac{2 \sin^{2}{\left(x \right)} + \cos{\left(2 x \right)}}{\cos^{2}{\left(x \right)}}\, dx\).
Question 19
Evaluate \(\int \frac{1}{\sin{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx\).
Question 20
Evaluate \(\int \frac{\cos{\left(2 x \right)}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}\, dx\).
Question 21
Integrate sin⁻¹(cos x).
Question 22
Evaluate \(\int \frac{1}{\cos{\left(a - x \right)} \cos{\left(b - x \right)}}\, dx\).
Question 23
Evaluate \(\int \frac{\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\…
Question 24
Evaluate \(\int \frac{\left(x + 1\right) e^{x}}{\cos^{2}{\left(x e^{x} \right)}}\, dx\).