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

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1. Evaluate:

14/3

1/2

12/5

12/7

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

32/3

34/11

43/8

23/4

3. Find the area of the finite region bounded by the curve y = 5 - 4x - x² and the lines y = 0, x= 0 and x = -5

100/3

9/2

3/100

2/9

4. Evaluate the integrals:

14/3

14

12

12/3

5. The gradient of the curve that passes through the point (1, -10) is given by 3x² - 6. Find the equation of the curve.

y = x³ + 5

y = x³ - 6x - 5

y = x³ + 6x - 5

y = x³ - 30

6. Find in square units, the area of the finite region bounded by the curve y = x³ - x and the x-axis, from x = -1 to x =1

1/4

2

1/2

1/3

7. Find ∫x² log x dx

C

x³/3 logx - x³/6 + C

x/4 + logx + C

xlogx + C

8. Evaluate the definite integral:

0

1

5

-1

9. Find ∫ sin x cos 3x dx

-1/8 cos4x + 1/4 cos2x + C

-1/8 cos4x + 1/4 sin2x + C

1/4 cos2x + C

1/8 cos4x + 1/4 sin2x + C

10. 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.

18 m

24 m

3 m

48 m

11. Find ∫ (2+x)/x dx, x > 0.

ln x³ +x + C

In 2x + C

In x² + x + C

In 2x + x + C

12. The gradient of a curve that passes through the point (-2, 6) is given by x. Determine the equation of the curve.

y = x² - 4

y = x² + 4

y = -1/2 x² - 4

y = 1/2 x² + 4

13. The acceleration of a particle moving in a straight line is given by a = 3t² - 4t. Find the expressions for the velocity given that v = 0 m/s and t = 0 s.

v = 2t³ - t²

v = t³ - 2t

v = t³ + 2t²

v = t³ - 2t²

14. Find ∫ 1/ x(x+1) dx

In(x-1) + C

In(x / x+1) + C

In(x+1) +C

In(x / x-1) + C

15. Find the area of the curve y = 2x² + 5, x-axis from 0 and 3

14

22

33

53

16. Evaluate:

11/3

13/3

10/3

4

17. Find the area bounded by the curve y = x(2 - x), the x-axis, x=0 and x= 2.

3

4/3

2

4

18. Find the area bounded by the given pairs of curves y = x² - x + 3 and y = 3

1/3

1/2

1/5

1/6

19. The gradient of a curve at P(x, y) is 3x². If the curve passes through Q(1, 5), find the equation of the curve.

3x³+4

x³+4x

x+4

x³+4

20. 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(2, 5), N(3, 18)

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

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

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

21. Evaluate the integrals:

1

0

-1

2

22. With the curve y = (x-3)². Find the area of the finite region enclosed between the curve and the x and y axes

9

11

9/3

4

23. The velocity of a particle is given by v =3t² + 8t. Find the acceleration when t = 8s

8 m/s²

18 m/s²

23 m/s²

56 m/s²

24. Find ∫ x / 2x+3 dx

1/2 x -3/4 In(2x+3)

In(2x+3) + C

1/2 x -3/4 In(2x+3) + C

1/2 x +C

25. Find the area bounded by the curve y = x³ -3x² -x + 3 and the x-axis