Integral Calculus

Integral Calculus

One Mark Questions

PREPARED BY:R.RAJENDRAN. M.A., M. Sc., M. Ed.,K.C.SANKARALINGA NADAR HR. SEC. SCHOOL,CHENNAI-21

Choose the Correct Answer

1. The value of is

(a) (b)

(c) 0 (d)

2. The value of is

(a) (b) 0

(c) (d)

2/

03/53/5

3/5

sincos

cos

dxxx

x

2

4

2

4

2/

0 cossin1

cossin

dxxx

xx


3. The value of is

(a) (b)

(c) (d)

4. The value of is

(a) 0 (b) 2

(c) log2 (d) log4

1

0

4)1( dxxx

12

1

30

1

2/

2/ cos2

sin

dxx

x24

120

1


5. The value of is

(a) (b)

(c) 0 (d)

6. The value of is

(a) (b) 0

(c) (d)

0

4sin xdx

16

316

3

3

2

3

2

4/

0

3 2cos

xdx8

3

3

1

Choose the Correct Answer 7. The value of is

(a) (b)

(c) (d) 0

8. The area bounded by the line y = x, the x-axis, the

ordinates x = 1, x = 2 is

(a) (b)

(c) (d)

0

32 cossin xdxx

2

4

2

3

2

1

2

5

2

7

Choose the Correct Answer 9. The area of the region bounded by the graph of y = sin

x and y = cos x between x = 0 and x = /4 is

(a) 2 + 1 (b) 2 – 1

(c) 2 2 – 2 (d) 2 2 + 2

10. The area bounded by the parabola y2 = x and its latus rectum is

(a) (b)

(c) (d)

3

4

3

26

1

3

8

Choose the Correct Answer 11. The area between the ellipse and its auxiliary

circle is

(a) b(a – b) (b) 2a(a – b)

(c) a(a – b) (d) 2b(a – b)

12. The volume of the solid obtained by revolving about the minor axis is

(a) 48 (b) 64

(c) 32 (d) 128

12

2

2

2

b

y

a

x

1169

22

yx

Choose the Correct Answer 13. The volume, when the curve y = from x =

0 to x = 4 is rotated about x-axis is

(a) 100 (b)

(c) (d)

14. The volume generated when the region bounded by y = x, y = 1, x = 0 is rotated about x – axis is

(a) (b)

(c) (d)

4

3

3

2

23 x

3

100

9

100

3

100

2

Choose the Correct Answer 15. The volume of solid obtained by revolving the area of

the ellipse about major and minor axes are

in the ratio

(a) b2 : a2 (b) a2 : b2

(c) a : b (d) b : a

16. The volume generated by rotating the triangle with

vertices at (0, 0), (3, 0), (3, 3) about x – axis is

(a) 18 (b) 2

(c) 36 (d) 9

12

2

2

2

b

y

a

x

Choose the Correct Answer 17. The length of arc of the curve x2/3 + y2/3 = 4 is

(a) 48 (b) 24

(c) 12 (d) 96

18. The surface area of the solid of revolution of the region bounded by y = 2x, x = 0, x = 2 about x-axis is

(a) 85 (b) 25

(c) 5 (d) 45

Choose the Correct Answer 19. The area bounded by the parabola y2 = 4x and its latus

rectum is(a) 2/3 (b) 8/3

(c) 16/3 (d) 4/3

20. The curved surface area of a sphere of radius 5, intercepted between two parallel planes of distance 2 and 4 from the center is (a) 20 (b) 40

(c) 10 (d) 30


21. If then

(a) f(2a – x) = f(x) (b) f(a – x) = f(x)

(c) f(x) = – f(x) (d) f(–x) = f(x)

22. If f(x) is an odd function then is

(a) (b)

(c) 0 (d)

aa

dxxfdxxf0

2

0

)(2)(

a

a

dxxf )(

a

dxxf0

)(2 a

dxxf0

)(

a

dxxaf0

)(


23. If n is odd then is

(a)

(b)

(c)

(d)

2/

0

sin

xdxn

25

4

3

2

1

n

n

n

n

n

n

22

1

4

5

2

31

n

n

n

n

n

n

12

3

5

4

3

2

1

n

n

n

n

n

n

13

2

4

5

2

31

n

n

n

n

n

n


24. If n is even then is

(a)

(b)

(c)

(d)

2/

0

sin

xdxn

25

4

3

2

1

n

n

n

n

n

n

22

1

4

5

2

31

n

n

n

n

n

n

12

3

5

4

3

2

1

n

n

n

n

n

n

13

2

4

5

2

31

n

n

n

n

n

n


25. If n is odd then is

(a)

(b)

(c)

(d)

2/

0

cos

xdxn

25

4

3

2

1

n

n

n

n

n

n

22

1

4

5

2

31

n

n

n

n

n

n

12

3

5

4

3

2

1

n

n

n

n

n

n

13

2

4

5

2

31

n

n

n

n

n

n


26. If n is even then is

(a)

(b)

(c)

(d)

2/

0

cos

xdxn

25

4

3

2

1

n

n

n

n

n

n

22

1

4

5

2

31

n

n

n

n

n

n

12

3

5

4

3

2

1

n

n

n

n

n

n

13

2

4

5

2

31

n

n

n

n

n

n

Choose the Correct Answer27. The area bounded by the curve x = g(y) to the right of

y-axis and the two lines y = c and y = d is given by

(a) (b) (c) (d)

28. The area bounded by the curve x = f(y), y-axis and the

lines y = c and y = d is rotated about y – axis. Then the

volume of the solid is

(a) (b) (c) (d)

d

c

dxx a

c

dyx d

c

dyy d

c

dyx

d

c

dyx 2 d

c

dxx 2 d

c

dxy 2 d

c

dyy 2

Choose the Correct Answer29. The area bounded by the curve x = g(y) to the left of

y-axis and the two lines y = c and y = d is given by

(a) (b) (c) (d)

30. The area bounded by the curve y = f(x), x-axis and the

lines x = a and x = b is rotated about x – axis. Then the

volume of the solid is

(a) (b) (c) (d)

d

c

dxy d

c

dyx d

c

dxy d

c

dyx

d

c

dyx 2 d

c

dxx 2 d

c

dxy 2 d

c

dyy 2


31. The arc length of the curve y = f(x) from x = a and

x = b is

(a) (b)

(c) (d)

b

a

dxdx

dy 1

2

d

c

dxdy

dx 1

2

b

a

dxdx

dyy 12

2

b

a

dxdy

dxy 12

2


32. The surface area obtained by revolving the area

bounded by the curve y = f(x) from x = a and

x = b and x-axis, about x-axis is

(a) (b)

(c) (d)

b

a

dxdx

dy 1

2

d

c

dxdy

dx 1

2

b

a

dxdx

dyy 12

2

b

a

dxdy

dxy 12

2


33. The area of the region bounded by the line y + 3 = x,

x = 1 and x = 5 is

(a) 3sq.units (b) 4sq.units

(c) 0sq.units (d) 5sq.units

34. The length of the arc of the curve x = a(t – sint),

y = a(1 – cost) between t = 0 and t = is

(a) 8a (b) 6a

(c) 4a (d) 3a

Choose the Correct Answer35. The area of the curve y2 = (x – 5)2 (x – 6) between x = 5

and x = 6 is

(a) 0sq.units (b) 1sq.units

(c) 4sq.units (d) 6sq.units

36. The volume of the solid that results when the region

enclosed by is revolved about the major

axis (a > b > 0) is

(a) (b)

(c) (d)

12

2

2

2

b

y

a

x

2ab 8

4 ba 3

4 2

2ab 3

4 ba 4

3 2


37. The volume of the solid that results when the region

enclosed by is revolved about the minor

axis (a > b > 0) is

(a) (b)

(c) (d)

12

2

2

2

b

y

a

x

2ab 8

4 ba 3

4 2

2ab 3

4 ba 4

3 2


38. The surface area of the solid generated by revolving the

arc of the parabola y2 = 4ax bounded by its LR about

x-axis is

(a) (b)

(c) (d)

1223

8 2

a 122

3

4 2

a

1223

2

a 122

3

8 2

a

Choose the Correct Answer39. The total length of the curve x2/3 + y2/3 = a2/3 is

(a) 3a (b) 4a

(c) 6a (d) 8a

40. The area of the region bounded by the ellipse

is

(a) 2a2sq.units (b) 2b2sq.units

(c) 2ab sq.units (d) ab sq.units

12

2

2

2

b

y

a

x

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Integral Calculus