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

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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) = 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: