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:

1/3

1/2

-1/3

-1/2

2. Find
∫ 1 / x²-7x+10 dx

In(x-5) + C

1/3 In(x-5 / x-2) + C

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

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

4/3

3/4

3/2

2/3

4. Evaluate
∫ x / x+3 dx

x - 3 In(x+3) + C

In(x + 3) + C

x-3 + C

5. 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 = x - 18

y = x² - 6x - 5

y = x² - 6x - 3

y = x² - 6x

6. 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 - 6x - 5

y = x³ + 5

y = x³ + 6x - 5

y = x³ - 30

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

y = 1/3 x³ + 5/3

y = 1/3 x³ - 5/3

y = 3x³ + 3/5

y = x³ + 2x

8. Evaluate:

19/3

6/157

157/6

3/19

9. ∫(sinx- 5cosx)dx

-cosx -5sinx + C

cosx - 2sinx + C

cosx + 5sinx + C

sinx + C

10. 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

11. Evaluate:

In 4

In 3

In 7

In 6

12. 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

13. 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?

12 m/s

24 m/s

4 m/s

0.5 m/s

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

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

32/3

24.7

16. Find
∫x cos2x dx

1/2 x sin2x + C

cos4x + C

1/2 x sin 2x + 1/4 cos 2x + C

17. 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

(0, 6)

(2, 9)

(1, 7)

(3, 1)

18. The table below shows the velocity V m/s of a particle in a relation to time t s within a period of t seconds

t 0 1 2 3 4 5 6
V 10 12 15 16 11 5 3

Use trapezoid rule:
1/2 h(y1 +2y2 + 2y3 + ... + yn)
Find the approximate distance traveled

6.5 sq. units

63.5 sq units

65.5 sq. units

60.5 sq. units

19. 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.

147 m

32 m

132 m

47 m

20. ∫sin 5x dx

1/5sinx + C

-1/5 cos5x + C

-1/5 sin 5x + C

1/5cos5x + C

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

14 m/s²

26 m/s²

54 m/s²

37 m/s²

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

(1, 2)

(4, 0)

(11/3, 9)

(1, 7/3)

23. 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

24. 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?

138 m

144 m

168 m

112 m

25. Find
∫ x / 2x+3 dx

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

1/2 x +C

In(2x+3) + C

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

26 out of 25