## Rajasthan Board RBSE Class 12 Maths Chapter 9 Integration Ex 9.2

Question 1.

Integrate the following w.r.t.x :

(a) x sin x^{2}

(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) ∫ cos^{4} x dx

(b) ∫ sin^{3} 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 | + C_{1}

= (x + a) cos 2a – sin 2a log | sin (x + a) | + C_{1}

= x cos 2a – sin 2a log | sin (x + a) | + a cos 2a + C_{1}

= x cos 2a – sin 2a log | sin (x + a) | + C

( where C = a cos 2a + C_{1})

Question 13.

Find the following :

Solution:

Question 14.

Find the following :

Solution:

Question 15.

Find the following :

Solution:

Question 16.

Solution:

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