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

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1.

Evaluate the integrals:

11

12

3

6

None

2.

Find ∫sin2x sin3x dx

1/10 sin5x + 1/2 sinx + C

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

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

1/2 cosx + C

None

3.

Find ∫x² log x dx

x³/3 logx - x³/6 + C

C

xlogx + C

x/4 + logx + 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(0, 4), N(4, 18)

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

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

M(2, 5), N(3, 18)

None

5.

Given that dv/dt = -64t and v = 10 when t = 0, find v when t = 2.

v = 64

v = 118

v = -64

v = -118

None

6.

Evaluate the definite integral:

-10/3

12/5

-3

-4

None

7.

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

2

4/3

3

4

None

8.

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

y³/3 - 2x² + 3x + 6

y³/3 - 2x²

y³/3 - 2x² + 3x + 1

2x² + 3x + 1

None

9.

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

38 sq. units

284/3 sq. units

2237 sq. units

3/38 sq. units

None

10.

Evaluate the definite integral:

56

35

81

102

None

11.

An object is ejected vertically upwards from the ground at 18 m/s. Find the height of the object after 3 s.

60m

54 m

48 m

84 m

None

12.

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

9/3

11

4

9

None

13.

Find ∫x cos2x dx

cos4x + C

1/2 x sin2x + C

C

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

None

14.

Evaluate:

10/3

4

13/3

11/3

None

15.

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 = x³ + 2x²+ 3x

y = x²+ 3x - 2

None

16.

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 - 30

y = x³ + 6x - 5

None

17.

Find ∫ 1/ x(x+1) dx

In(x+1) +C

In(x-1) + C

In(x / x-1) + C

In(x / x+1) + C

None

18.

Evaluate the definite integral:

2456.63

456.43

324.87

1658.57

None

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

47 m

32 m

132 m

None

20.

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

26 m/s²

37 m/s²

14 m/s²

54 m/s²

None

21.

The velocity of a particle is given by v =3t² + 8t. Find the distance travelled by the particle between t = 3 s and t = 5 s.

162 m

224 m

158 m

144 m

None

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

None

23.

Find ∫ 1/ x²+3x-10 dx

7In x + C

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

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

C

None

24.

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