Welcome to your Integration(Senior Class Math Study by Topics)

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1. Evaluate the integrals:

10

6

20

13

2. A body is projected from a point O in a straight line with an initial velocity of 10 m/s. If the acceleration is 5t² + 3t, find the distance from 0 at this instant

21.54 m

54.75 m

12.47 m

43.45 m

3. Calculate the area under the line y = x + 2 between the limits x = 0 and x = 10

55

60

70

50

4. Evaluate the definite integral:

102

35

81

56

5. Evaluate:

13/3

4

11/3

10/3

6. A particle moves in a straight line with a velocity v in m/s at time t is given by v = 3t² +10. Calculate the distance it travels from t = 2s to t = 5s.

132 m

47 m

32 m

147 m

7. The acceleration of a moving particle at the end of t seconds is given by (5 - t) m/s². If the particle starts from rest, find its velocity at the end of 4 s?

4 m/s

0.5 m/s

12 m/s

24 m/s

8. Calculate the area of the finite region bounded by the curve y = 4x - x² and the x-axis

23/4

43/8

34/11

32/3

9. The gradient of a curve which passes through the point ( 1, 2) is given by x². Determine the equation of the curve.

y = 3x³ + 3/5

y = 1/3 x³ + 5/3

y = x³ + 2x

y = 1/3 x³ - 5/3

10. The gradient of a curve at any point (x, y) is given by dy/dx = 2(x - 3) and the point(3, -12) lies on the curve. Find the equation of the curve.

y = x² - 6x - 5

y = x² - 6x

y = x - 18

y = x² - 6x - 3

11. Given that y and x are two variables such that dy/dx = 2x - 6, and y = -1 when x = 3, express y in terms of x.

y = x² - 6x + 8

y = x² + 6

y = x² + 6x + 8

y = x - 3

12. Evaluate ∫1/x(x + 2) dx, x ≠ 0, -2

1/2 In(x / x+2) + C

x + 2 + C

2In(x+2 / x) + C

x/2 + C

13. Find the area bounded by the curve y =x(x - 1) and the line y = 3x

32/3

35

11

23

14. Calculate the area of the finite region bounded by the curve y = x² + 4x - 12, the x-axis and the ordinates x = 1 and x = 3

8

6

4

2

15. The gradient of a curve is given by x² - 4x + 3 If the curve passes through the point (3, 1). Find the area of the finite region enclosed by the curve, the lines x = 1, x = 3 and y = 0

5/9

6/7

10/3

8/7

16. Find ∫x sin 2x dx

sin2x /2 + C

-xcos2x /2 + sin2x /2+ C

xcos2x /2 + sin2x /2 + C

cos2x /2 + C

17. A line with equation y = 4x + 2 intersects a curve with the equation y = x² + 2 at the points M and N. Determine the coordinates of M and N

M(1, 3), N(3, 12)

M(2, 5), N(3, 18)

M(2, 3), N(2, 5)

M(0, 4), N(4, 18)

18. The velocity v m/s of a body moving at any time t, is given by v = 2t² - 1/3t³ + 10, determine the values of t at which the acceleration of the particle is zero.

1/2s, 2.4s

3s, 5s

0s, 4s

-2s, 9s

19. The velocity of a particle, v m/s, after t s is given by v = t² + 5. Find the distance travelled at the end of 3 s.

24 m

18 m

48 m

3 m

20. Evaluate the integrals:

14/3

12/3

12

14

21. Evaluate:

6- 2In5

8In 5

10/3 - 5In3

4/5In 3

22. A curve passes through the point (3, -1). If its gradient function is 2x + 5, find the equation of the curve

y = 3x³ + 5x - 25

y = 3x³ + x² + 5x + 25

y = 3x³ + x² + 5x - 25

y = x² + 5x - 25

23. Find ∫x tan²x dx

Incos x+C

x(tanx- x) +In cosx + C

x(tanx- x) +In cosx + x²/2 + C

x(tanx -x) + C

24. Find the area of the region lying below the x-axis and bounded by the parabola y = x(x - 2) and the x-axis.

3/4

2/3

4/3

3/2

25. The gradient of a curve at any point (x,y) is 6x² - 6x + 11. If the curve passes through the point (3, 0), find its equation