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## 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) = x^{3} sin^{2} x = x^{3} (sin x)^{2}

∴f(-x) = (-x)^{3} (sin (-x))^{2} = (-x)^{3} (-sin x)^{2}

= – x^{3} sin^{2} 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: