# Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3

## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3

Question 1.
Evaluate the following definite integrals :
(i)
Solution:

(ii)
Solution:

(iii)
Solution:

(iv)
Solution:

(v)
Solution:

(vi)
Solution:

Question 2.
Evaluate the following integrals using properties of integration :
(i)
Solution:

(ii)
Solution:

(iii)
Solution:

(iv)
Solution:

(v)
Solution:

(vi)
Solution:

(vii)
Solution:

(viii)
Solution:

(ix)
Solution:

(x)
Solution:

(xi)
Solution:

### Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 Additional Problems

Question 1.

Solution:
Let f (x) = x3 sin2 x = x3 (sin x)2
∴f(- x) = (- x)3 (sin (- x))2 = (- x)3 (- sin x)2
= – x3 sin2 x = -f(x)
f(-x) = -f(x) ∴ f(x) is an odd function.

Question 2.

Solution:

Question 3.

Solution:
Let f(x) = x sin x
f(-x) = (-x)sin(-x)
= x sin x (∵ sin(-x) = – sin x)
∴ f(x) is an even function

Question 4.

Solution:

Question 5.

Solution: