NCERT Class 12 Maths
Chapter 7: Integrals
22 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.1
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Evaluate \(\int \sin{\left(2 x \right)}\, dx\).
Question 2
Evaluate \(\int \cos{\left(3 x \right)}\, dx\).
Question 3
Evaluate \(\int e^{2 x}\, dx\).
Question 4
Evaluate \(\int \left(a x + b\right)^{2}\, dx\).
Question 5
Evaluate \(\int \left(- 4 e^{3 x} + \sin{\left(2 x \right)}\right)\, dx\).
Question 6
Evaluate \(\int \left(4 e^{3 x} + 1\right)\, dx\).
Question 7
Evaluate \(\int x^{2} \left(1 - \frac{1}{x^{2}}\right)\, dx\).
Question 8
Evaluate \(\int \left(a x^{2} + b x + c\right)\, dx\).
Question 9
Evaluate \(\int \left(2 x^{2} + e^{x}\right)\, dx\).
Question 10
Evaluate \(\int \left(\sqrt{x} - \frac{1}{\sqrt{x}}\right)^{2}\, dx\).
Question 11
Evaluate \(\int \frac{x^{3} + 5 x^{2} - 4}{x^{2}}\, dx\).
Question 12
Evaluate \(\int \frac{x^{3} + 3 x + 4}{\sqrt{x}}\, dx\).
Question 13
Evaluate \(\int \frac{x^{3} - x^{2} + x - 1}{x - 1}\, dx\).
Question 14
Evaluate \(\int \sqrt{x} \left(1 - x\right)\, dx\).
Question 15
Evaluate \(\int \sqrt{x} \left(3 x^{2} + 2 x + 3\right)\, dx\).
Question 16
Evaluate \(\int \left(2 x + e^{x} - 3 \cos{\left(x \right)}\right)\, dx\).
Question 17
Evaluate \(\int \left(5 \sqrt{x} + 2 x^{2} - 3 \sin{\left(x \right)}\right)\, dx\).
Question 18
Evaluate \(\int \left(\tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)}\, dx\).
Question 19
Evaluate \(\int \frac{\sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\, dx\).
Question 20
Evaluate \(\int \frac{2 - 3 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\, dx\).
Question 21
Evaluate \(\int \left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)\, dx\).
Question 22
Find f if f′(x)=4x³−3/x⁴ and f(2)=0.