Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

You can Download Samacheer Kalvi 12th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Choose the correct or the most suitable answer from the given four alternatives:

Question 1.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 1
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 2
Solution:
(a) \(\frac{\pi}{6}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 3

Question 2.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 4
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 5
Solution:
(c) \(\frac{5}{2}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 7

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Question 3.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 8
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 9
Solution:
(c) 0
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 10

Question 4.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 11
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 12
Solution:
(d) \(\frac{2}{3}\)
Hint:
It is an even function
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 13

Question 5.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 14
(b) 2π
(c) 3π
(d) 4π
Solution:
(d) 4π
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 144

Question 6.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 15
(a) 4
(b) 3
(c) 2
(d) 0
Solution:
(c) 2
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 155

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Question 7.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 16
(a) cos x – x sin x
(b) sin x + x cos x
(c) x cos x
(d) x sin x
Solution:
(c) x cos x
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 166

Question 8.
The area between y2 = 4x and its latus rectum is ………
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 17
Solution:
(c) \(\frac{8}{3}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 18
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 19

Question 9.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 20
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 21.
Solution:
(b) \(\frac{1}{10100}\)
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 22

Question 10.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 23
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 24
Solution:
(a) \(\frac{\pi}{2}\)
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 25

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Question 11.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 26
(a) 10
(b) 5
(c) 8
(d) 9
Solution:
(d) 9
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 27

Question 12.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 28
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 29
Solution:
(b) \(\frac{2}{9}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 30

Question 13.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 31
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 32
Solution:
\(\frac{3 \pi}{8}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 33

Question 14.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 34
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 35
Solution:
(d) \(\frac{2}{27}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 36

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Question 15.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 37
(a) 4
(b) 1
(c) 3
(d) 2
Solution:
(d) 2
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 38

Question 16.
The volume of solid of revolution of the region bounded by y2 = x(a – x) about x-axis is ……..
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 39
Solution:
(d) \(\frac{\pi a^{3}}{6}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 40

Question 17.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 41
(a) 3
(b) 6
(c) 9
(d) 5
Solution:
(c) 9
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 42

Question 18.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 43
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 44
Solution:
(d) \(\frac{\pi^{2}}{4}-2\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 45

Question 19.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 46
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 47
Solution:
(b) \(\frac{3 \pi a^{4}}{16}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 48

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Question 20.
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 49
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 50
Solution:
(a) \(\frac{1}{2}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 51

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 Additional Problems

Choose the correct or the most suitable answer from the given four alternatives:

Question 1.
The area bounded by the line y = x, the x – axis, the ordinates x = 1,x = 2 is …….
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 52
Solution:
(a) \(\frac{3}{2}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 53

Question 2.
The area of the region bounded by the graph of y = sin x and y = cos x between x = 0 and x = \(\frac{\pi}{4}\) is ……..
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 54
Solution:
(b) \(\sqrt{2}-1\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 55

Question 3.
The area between the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1 and its auxiliary circle is …….
(a) πb(a – b)
(b) 2πa(a – b)
(c) πa(a – b)
(d) 2πb(a – b)
Solution:
(c) πa(a – b)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 56

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Question 4.
The area bounded by the parabola y2 = x and its latus rectum is ……..
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 57
Solution:
(b) \(\frac{1}{6}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 58

Question 5.
The volume of the solid obtained by revolving \(\frac{x^{2}}{9}+\frac{y^{2}}{16}\) = 1 about the minor axis is …….
(a) 48π
(b) 64π
(c) 32π
(d) 128π
Solution:
(b) 64π
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 59
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 60

Question 6.
The volume, when the curve y = \(\sqrt{3+x^{2}}\) from x = 0 to x = 4 is rotated about x – axis is ……
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 61
Solution:
(c) \(\frac{100}{3} \pi\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 62

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Question 7.
The volume generated when the region bounded by y = x, y = 1, x = 0 is rotated about y – axis is ……….
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 63

Solution:
(c) \(\frac{\pi}{3}\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 64

Question 8.
Volume of solid obtained by revolving the area of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1 about major and minor axes are in the ratio …….
(a) b2 : a2
(b) a2 : b2
(c) a : b
(d) b : a
Solution:
(d) b : a
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 65

Question 9.
The volume generated by rotating the triangle with vertices at (0, 0), (3, 0) and (3, 3) about x-axis is …….
(a) 18π
(b) 2π
(c) 36π
(d) 9π
Solution:
(d) 9π
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 66

Question 10.
The length of the arc of the curve Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 611 is …….
(a) 48
(b) 24
(c) 12
(d) 96
Solution:
(a) 48
Hint:
Length of the arc of the curve = 6a
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 67
∴ Required length = 6a = 6 × 8 = 48 units.

Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Question 11.
The surface area of the solid of revolution of the region bounded by y = 2x, x = 0 and x = 2 about x-axis is ……
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 68
Solution:
(a) \(8 \sqrt{5} \pi\)
Hint:
Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10 69

Question 12.
The curved surface area of a sphere of radius 5, intercepted between two parallel planes of distance 2 and 4 from the centre is ……
(a) 20π
(b) 40π
(c) 10π
(d) 30π
Solution:
(a) 20π
Hint:
The curved surface area of a sphere of radius r intercepted between two parallel planes at a distance a and b from the centre of the sphere is 2πr (b – a)
Given radius, r = 5; a = 2; b = 4
Required surface area = 2πr (b – a)
= 2π × 5 × (4 – 2) = 20π sq. units