NCERT Solutions Class 12 Mathematics Chapter 7 Integrals

Exercise 7.1

1. Find an anti derivative (or integral) of the following functions by the method of inspection.
sin 2x . 
Answer :
The anti derivative of sin 2x is a function of x whose derivative is sin 2x.
It is known that,

Therefore, the anti derivative of sin2x is -1/2 cos 2x

2. Find an anti derivative (or integral) of the following functions by the method of inspection.
cos 3x . 
Answer :
The anti derivative of cos 3x is a function of x whose derivative is cos 3x.
It is known that,

3. Find an anti derivative (or integral) of the following functions by the method of inspection.
e^2x.
Answer :
The anti derivative of e^2x is the function of x whose derivative is e^2x.
It is known that,

4. Find an anti derivative (or integral) of the following functions by the method of inspection.
(ax + b)²
Answer :
The anti derivative of (ax + b)² is the function of x whose derivative is (ax + b)² . 
It is known that, 

5. Find an anti derivative (or integral) of the following functions by the method of inspection
sin 2x – 4 e^3x. 
Answer :
The anti derivative of (sin2x - 4e^3x) is the function of x whose derivative is (sin 2x - 4e^3x). 
It is known that, 

6. Find the following integrals ∫(4 e^3x + 1) dx
Answer :

7. Find the following integrals ∫[x² (1 - 1/x² ) dx 
Answer :

8. Find the following integrals ∫(ax + bx + c) dx .
Answer :

9. Find the following integrals ∫(2x² + e^x ) dx .
Answer :

10. Find the following integrals ∫ (√x - 1/√x)² dx
Answer :

11. Find the following integrals ∫[(x³ + 5x² - 4)/x² ] dx 
Answer :