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

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1. Evaluate ∫1/x(x + 2) dx, x ≠ 0, -2

x/2 + C

2In(x+2 / x) + C

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

x + 2 + C

2. Given that dy/dx = 6x² + 5x, find the function which passes through the point (2, 30).

y = 2x³ + 5/2 x² + 4

y = x³ + 2x² + 4

y = 6x² + 5x

y = 2x³ + 5/2 x² - 4

3. Evaluate the definite integral:

324.87

456.43

2456.63

1658.57

4. Evaluate the integrals:

1/2

-1/2

1/5

-1/5

5. 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 = x - 3

y = x² + 6

y = x² + 6x + 8

6. The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the point (-1, 10), find the equation of the curve

y = x² -4

y = 5x² - x³ + 4

y = 5x² - x³

y = 5x³ - x² + 8

7. Find ∫sin 2x cos 3x dx

-1/10 sin5x + 1/2 cosx + C

-1/10 cos5x + 1/2 cosx + C

1/2 cosx + C

1/10 cos5x + 1/2 cosx + C

8. 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

9. Find ∫1 / x(x-1) dx

In (x/ x+1) + C

In (x+1) + C

In (x-1) + C

In (x/ x-1) + C

10. A line with equation y = 4x + 2 intersects a curve with the equation y = x² + 2 at the points M and N. Evaluate the area enclosed between the curve and the line

21/4

32/3

11/2

12

11. Evaluate:

0.777

0.658

0.163

0.563

12. Evaluate:

correct to 3 decimal places

2.868

2.386

2.368

3.797

13. 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

3/100

9/2

100/3

2/9

14. The gradient of a curve which passes through the point (1, 2) is 3+2x. Find its equation.

y = x²+ 3x - 2

y = x³ + 2x² - 2

y = x³ + 2x²+ 3x

y = x³ + 2x²+ 3x - 2

15. An object travels in a straight line with velocity, v m/s at time t s is given by v = 3t² + 7. What is the distance travelled by the object from t = 2 s to t = 5 s?

168 m

144 m

138 m

112 m

16. The line 2y = x + 2 intersects the curve y = 1/4 (7x-x²). Calculate the area of the finite region bounded by the curve and the line

9/8

6/7

7/8

5/6

17. 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

9/3

4

11

18. Evaluate the integrals:

10

13

20

6

19. Evaluate:

157/6

6/157

3/19

19/3

20. Given that x and t are two variables such that dx/dt = 3t² - 4t, and x = 1 when t = 4, express x in terms of t.

x = 3t³ + 2t² - 31

x = 3t³ - 2t² - 31

x = t³ - 2t - 31

x = t³ - 2t² - 31

21. Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of

13 sq. units

12 sq. units

10 sq. units

11 sq. units

22. Find the area of the finite regions included between the curve in a curve y with gradient dy/dx = 3x² - 6x + 2 and the x-axis

2

1/4

1/3

1/2

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

53

14

22

33

24. 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