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) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 1
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 2

(ii) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 3
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 352

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

(iii) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 4
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 5
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 6

(iv) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 7
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 8

(v) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 88
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 9
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 10

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

(vi) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 11
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 12
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 13

Question 2.
Evaluate the following integrals using properties of integration :
(i) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 14
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 15

(ii) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 16
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 17
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 177

(iii) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 21
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 22

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

(iv) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 23
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 24

(v) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 25
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 26

(vi) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 27
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 28

(vii) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 29
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 30
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 31
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 32

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

(viii) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 33
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 34
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 35

(ix) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 36
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 37
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 38
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 39

(x) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 40
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 41
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 42

(xi) Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 44
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 45
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 455

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

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

Question 1.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 46

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.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 47

Question 2.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 48
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 49

Question 3.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 50
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
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 51

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

Question 4.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 52
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 53

Question 5.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 54
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 55
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3 56

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