RBSE Solutions for Class 12 Maths Chapter 9 Integration Ex 9.2

Rajasthan Board RBSE Class 12 Maths Chapter 9 Integration Ex 9.2

Question 1.
Integrate the following w.r.t.x :
(a) x sin x²
(b) x \(\sqrt { { x }^{ 2 }+1 } \)
Solution :

Question 2.
Find the following :

Solution:

Question 3.
Find the following :

Solution:

Question 4.
Find the following :

Solution:

Question 5.
Find the following :

Solution:

Question 6.
Find the following :

Solution:

Question 7.
Find the following :
(a) ∫ sin 3x sin 2x dx
(b) ∫ \(\sqrt { 1-sin x }\) dx
Solution:

Question 8.
Find the following :
(a) ∫ cos⁴ x dx
(b) ∫ sin³ x dx
Solution:

Question 9.
Find the following :

Solution:

Question 10.
Find the following :

Solution:

Question 11.
Find the following :

Solution:

Question 12.
Find the following :

Solution:

= cos 2a ∫ dt – sin 2a ∫ cot t dt
= (cos 2a)^t – sin 2a log | sin t | + C₁
= (x + a) cos 2a – sin 2a log | sin (x + a) | + C₁
= x cos 2a – sin 2a log | sin (x + a) | + a cos 2a + C₁
= x cos 2a – sin 2a log | sin (x + a) | + C
( where C = a cos 2a + C₁)

Question 13.
Find the following :

Solution:

Question 14.
Find the following :

Solution:

Question 15.
Find the following :

Solution:

Question 16.

Solution:

RBSE Solutions for Class 12 Maths