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

NAME

EMAIL

PHONE NUMBER

1.

Evaluate:

6- 2In5

8In 5

4/5In 3

10/3 - 5In3

2.

Evaluate:

1/3

-1/2

-1/3

1/2

3.

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

4.

Find the area bounded by the curve y =x(x - 1) and the line y = 3x

32/3

11

23

35

5.

Find the area bounded by the given pairs of curves y = x² - x + 3 and y = 3

1/2

1/3

1/6

1/5

6.

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

6/7

5/6

9/8

7.

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 = t³ - 2t² - 31

x = 3t³ - 2t² - 31

x = t³ - 2t - 31

8.

A body starting from the origin O moves in a straight line, and its velocity, v m/s, after t s is given by v = 12 + 20t - 3t². Calculate the distance moved by the particle in 2 s.

32 m

44 m

56 m

78 m

9.

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

3/2

2/3

3/4

4/3

10.

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 = 5x² - x³

y = x² -4

y = 5x³ - x² + 8

y = 5x² - x³ + 4

11.

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

11x-60

2x³-3x²+11x-60

2x³+11x-60

3x²+11x-60

12.

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 - 30

y = x³ + 6x - 5

y = x³ + 5

y = x³ - 6x - 5

13.

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 = x² + 6x + 8

y = x² + 6

y = x - 3

14.

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

32/3

12

21/4

11/2

15.

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

284/3 sq. units

3/38 sq. units

2237 sq. units

38 sq. units

16.

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

-2s, 9s

1/2s, 2.4s

0s, 4s

17.

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, 3), N(2, 5)

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

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

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

18.

Evaluate the integrals:

6

11

12

3

19.

Find ∫ x Inx dx

xe +C

xIn x + C

Inx + C

x² Inx - x²/4 + C

20.

Find ∫ x / 2x+3 dx

1/2 x +C

In(2x+3) + C

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

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

21.

The finite are enclosed by the curve y² = 4x and the line x = 4 is rotated through 360° about the x-axis. Find the volume of the solid generated in cubic units.

32π

27π

27

32

22.

Find in square units, the area of the finite region bounded by the curve y = x³ - x and the x-axis, from x = -1 to x =1

1/3

1/4

2

1/2

23.

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?

4 m/s

12 m/s

24 m/s

0.5 m/s

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