NCERT Class 12 Maths
Chapter 7: Integrals
24 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.6
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Evaluate \(\int x \sin{\left(x \right)}\, dx\).
Question 2
Evaluate \(\int x \sin{\left(3 x \right)}\, dx\).
Question 3
Evaluate \(\int x^{2} e^{x}\, dx\).
Question 4
Evaluate \(\int x \log{\left(x \right)}\, dx\).
Question 5
Evaluate \(\int x \log{\left(2 x \right)}\, dx\).
Question 6
Evaluate \(\int x^{2} \log{\left(x \right)}\, dx\).
Question 7
Evaluate \(\int x \operatorname{asin}{\left(x \right)}\, dx\).
Question 8
Evaluate \(\int x \operatorname{atan}{\left(x \right)}\, dx\).
Question 9
Evaluate \(\int x \operatorname{acos}{\left(x \right)}\, dx\).
Question 10
Evaluate \(\int \operatorname{asin}^{2}{\left(x \right)}\, dx\).
Question 11
Evaluate \(\int \frac{x \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}}}\, dx\).
Question 12
Evaluate \(\int x \sec^{2}{\left(x \right)}\, dx\).
Question 13
Evaluate \(\int \operatorname{atan}{\left(x \right)}\, dx\).
Question 14
Evaluate \(\int x \log{\left(x \right)}^{2}\, dx\).
Question 15
Evaluate \(\int \left(x^{2} + 1\right) \log{\left(x \right)}\, dx\).
Question 16
Evaluate \(\int \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) e^{x}\, dx\).
Question 17
Evaluate \(\int \frac{x e^{x}}{\left(x + 1\right)^{2}}\, dx\).
Question 18
Evaluate \(\int \frac{\left(\sin{\left(x \right)} + 1\right) e^{x}}{\cos{\left(x \right)} + 1}\, dx\).
Question 19
Evaluate \(\int \left(\frac{1}{x} - \frac{1}{x^{2}}\right) e^{x}\, dx\).
Question 20
Evaluate \(\int \frac{\left(x - 3\right) e^{x}}{\left(x - 1\right)^{3}}\, dx\).
Question 21
Evaluate \(\int e^{2 x} \sin{\left(x \right)}\, dx\).
Question 22
Integrate sin⁻¹(2x/(1+x²)).
Question 23
Evaluate \(\int x^{2} e^{x^{3}}\, dx\).
Question 24
Evaluate \(\int \left(\tan{\left(x \right)} + 1\right) e^{x} \sec{\left(x \right)}\, dx\).