Integration(Senior Class Math Study by Topics Test ) : GATE Academy

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

NAME

PHONE NUMBER

1. Evaluate:

283 sq. units

38/3 sq. units

48 sq. units

283/3 sq units

2. 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.

3s, 5s

1/2s, 2.4s

0s, 4s

-2s, 9s

3. 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

3x²+11x-60

2x³+11x-60

2x³-3x²+11x-60

11x-60

4. Evaluate the definite integral:

324.87

456.43

1658.57

2456.63

5. Evaluate:
∫ 1 / x²(1-4x)

Inx + C

4(x / 1-4x) + C

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

6. 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

6/7

5/9

10/3

8/7

7. Find the area bounded by the curve y = -5 + 6x - x² and the x-axis

32/3

24.7

8. A curve y has gradient
dy/dx = 3x² - 6x + 2.
If the curve passes through the origin,
find its equation.

y = 1-x

y = x(x+5)

y = x(x-1)(x-2)

y = x + 2

9. Find
∫1 / x(x-1) dx

In (x/ x+1) + C

In (x/ x-1) + C

In (x-1) + C

In (x+1) + C

10. Evaluate:

In 4

In 7

In 6

In 3

11. Find
∫ 1/ x²+3x-10 dx

1/7 In (x-2 / x-5) + C

7In x + C

In (x-2 / x-5) + C

12. Evaluate the integrals:

-1

13. 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

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

y = x³ + 2x²+ 3x - 2

y = x³ + 2x² - 2

y = x²+ 3x - 2

y = x³ + 2x²+ 3x

15. Find

∫(x + 1)(x² - 2)dx

x² - 2x + C

2x - x + C

x4/4 + x³/3 - x² - 2x + C

x³ + 2x + C

16. Find
∫ x / 2x+3 dx

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

In(2x+3) + C

1/2 x +C

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

17. 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

138 m

112 m

144 m

18. Evaluate:

10/3

11/3

13/3

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

y = -1/2 x² - 4

y = 1/2 x² + 4

y = x² + 4

y = x² - 4

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

54 m/s²

14 m/s²

37 m/s²

26 m/s²

21. Evaluate:

6- 2In5

10/3 - 5In3

4/5In 3

8In 5

22. The gradient of a curve is given by
x² - 4x + 3
If the curve passes through the point (3, 1).
Find the minimum point on the curve

(1, 7)

(2, 9)

(3, 1)

(0, 6)

23. 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

12.47 m

43.45 m

54.75 m

24. Evaluate the definite integral:

12/5

-3

-10/3

-4

25. Evaluate the integrals:

12/3

14/3

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