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

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PHONE NUMBER

1.

Evaluate:

48 sq. units

283/3 sq units

283 sq. units

38/3 sq. units

2.

Evaluate:

157/6

6/157

19/3

3/19

3.

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.

1/2s, 2.4s

0s, 4s

3s, 5s

-2s, 9s

4.

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)

(11/3, 9)

(4, 0)

(1, 7/3)

5.

Evaluate ∫ x / x+3 dx

In(x + 3) + C

C

x-3 + C

x - 3 In(x+3) + C

6.

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.

158 m

224 m

162 m

144 m

7.

Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of

10 sq. units

12 sq. units

11 sq. units

13 sq. units

8.

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

y = x(x+5)

y = x + 2

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

y = 1-x

9.

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 = 5x³ - x² + 8

y = x² -4

y = 5x² - x³ + 4

10.

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

65.5 sq. units

60.5 sq. units

63.5 sq units

6.5 sq. units

11.

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 + 1

y³/3 - 2x²

2x² + 3x + 1

y³/3 - 2x² + 3x + 6

12.

Find ∫ 1 / x²-7x+10 dx

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

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

C

In(x-5) + C

13.

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

2237 sq. units

284/3 sq. units

3/38 sq. units

38 sq. units

14.

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

1/2

1/3

1/4

15.

A curve passes through the point (3, -1). If its gradient function is 2x + 5, find the equation of the curve

y = 3x³ + x² + 5x + 25

y = 3x³ + 5x - 25

y = x² + 5x - 25

y = 3x³ + x² + 5x - 25

16.

Evaluate:

12/5

12/7

14/3

1/2

17.

Evaluate the integrals:

12

11

6

3

18.

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?

144 m

138 m

168 m

112 m

19.

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

6/7

5/6

7/8

9/8

20.

Find ∫ 1/ x(x+1) dx

In(x+1) +C

In(x / x-1) + C

In(x-1) + C

In(x / x+1) + C

21.

Evaluate the integrals:

13

10

6

20

22.

The gradient of a curve is given by dy/dx = 3x² - 8x + 3. If the curve passes through the origin, find the equation of the curve.

y = x³

y = x³ - 4x² + 3x

y = x³ + 3x

y = x³ - 4x² - 3x

23.

Calculate the area of the finite region bounded by the curve y = x² + 4x - 12, the x-axis and the ordinates x = 1 and x = 3

4

8

2

6

24.

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