1. Integral Calculus One Mark Questions

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

3. 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

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

5. 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)

6. 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)

7. 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 

8. 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)

9. 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 

10. 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 

11. 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 

12. 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)

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

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

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

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

17. 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)

18. 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)

19. 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)

20. 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)

21. 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

22. 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)

23. 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)

24. 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)

25. 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