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

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1.

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

112 m

138 m

144 m

None

2.

∫(sinx- 5cosx)dx

-cosx -5sinx + C

sinx + C

cosx + 5sinx + C

cosx - 2sinx + C

None

3.

Find ∫ 1/ x(x+1) dx

In(x / x-1) + C

In(x / x+1) + C

In(x+1) +C

In(x-1) + C

None

4.

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

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

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

None

5.

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 = t³ - 2t²

v = t³ - 2t

v = 2t³ - t²

v = t³ + 2t²

None

6.

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

43.45 m

54.75 m

12.47 m

None

7.

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

2x³+11x-60

11x-60

2x³-3x²+11x-60

3x²+11x-60

None

8.

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)

(3, 1)

(0, 6)

(2, 9)

None

9.

Evaluate the definite integral:

12/5

-4

-10/3

-3

None

10.

Find, in square units, the area of the finite region bounded by the curve

y = x² + 4x + 2, and lines y = 0, x = 4 and x = 6

3/38 sq. units

2237 sq. units

38 sq. units

284/3 sq. units

None

11.

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+ 3x

y = x³ + 2x² - 2

y = x²+ 3x - 2

None

12.

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

8

2.1

4

3.3

None

13.

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 velocity after 3 seconds.

68.5 m/s

48 m/s

58.5 m/s

60 m/s

None

14.

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.

3 m

18 m

48 m

24 m

None

15.

Find ∫x² log x dx

C

x³/3 logx - x³/6 + C

x/4 + logx + C

xlogx + C

None

16.

Evaluate:

4

10/3

11/3

13/3

None

17.

Evaluate: ∫ 1 / x²(1-4x)

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

4(x / 1-4x) + C

C

Inx + C

None

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.

0s, 4s

1/2s, 2.4s

-2s, 9s

3s, 5s

None

19.

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

37 m/s²

26 m/s²

54 m/s²

14 m/s²

None

20.

Evaluate:

6/7

7/6

2/3

3/2

None

21.

Evaluate:

0.658

0.163

0.563

0.777

None

22.

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

7/8

5/6

9/8

6/7

None

23.

Evaluate the definite integral:

35

81

56

102

None

24.

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?