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Integral Calculus One Mark Questions

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Choose the Correct Answer 1. The value of is (a) (b) (c) 0(d) 2. The value of is (a) (b) 0 (c) (d)

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Choose the Correct Answer 3. The value of is (a) (b) (c) (d) 4. The value of is (a) 0(b) 2 (c) log2 (d) log4

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Choose the Correct Answer 5. The value of is (a) (b) (c) 0(d) 6. The value of is (a) (b) 0 (c) (d)

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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)

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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 y 2 = x and its latus rectum is (a) (b) (c) (d)

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Choose the Correct Answer 11. The area between the ellipse and its auxiliary circle is (a) b(a – b)(b) 2 a(a – b) (c) a(a – b) (d) 2 b(a – b) 12. The volume of the solid obtained by revolving about the minor axis is (a) 48 (b) 64 (c) 32 (d) 128

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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)

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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) b 2 : a 2 (b) a 2 : b 2 (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

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Choose the Correct Answer 17. The length of arc of the curve x 2/3 + y 2/3 = 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) 8 5 (b) 2 5 (c) 5 (d) 4 5

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Choose the Correct Answer 19. The area bounded by the parabola y 2 = 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

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Choose the Correct Answer 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)

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Choose the Correct Answer 23. If n is odd then is (a) (b) (c) (d)

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Choose the Correct Answer 24. If n is even then is (a) (b) (c) (d)

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Choose the Correct Answer 25. If n is odd then is (a) (b) (c) (d)

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Choose the Correct Answer 26. If n is even then is (a) (b) (c) (d)

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Choose the Correct Answer 27. 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)

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Choose the Correct Answer 29. 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)

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Choose the Correct Answer 31. The arc length of the curve y = f(x) from x = a and x = b is (a) (b) (c) (d)

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Choose the Correct Answer 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)

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Choose the Correct Answer 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

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Choose the Correct Answer 35. The area of the curve y 2 = (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)

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Choose the Correct Answer 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)

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Choose the Correct Answer 38. The surface area of the solid generated by revolving the arc of the parabola y 2 = 4ax bounded by its LR about x-axis is (a) (b) (c) (d)

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Choose the Correct Answer 39. The total length of the curve x 2/3 + y 2/3 = a 2/3 is (a) 3a (b) 4a (c) 6a (d) 8a 40. The area of the region bounded by the ellipse is (a) 2 a 2 sq.units (b) 2 b 2 sq.units (c) 2 ab sq.units (d) ab sq.units

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