Free Printable Integration 2

1.

Evaluate: $\int_{-2}^6xdx$

(a)

2.

Find the average value of the function $f\left(x\right)=x+3$ on the interval $\left[3,9\right]$

a)

$54$

b)

$67.5$

c)

$7.5$

d)

$9$

3.

$\int_0^6\left(\frac{1}{2}x-2\right)dx=$

(a)

4.

Find the average value of $f\left(x\right)=6-2x$ on $\left[-1,4\right]$

a)

3

b)

3.2

c)

10

d)

15

5.

Evaluate the definite integral.

a)

3

b)

9/2

c)

9

d)

Not possible

6.

_{Evaluate the integral}

a)

30/3

b)

31/3

c)

29/3

d)

32/3

7.

a)

12/3

b)

6.5

c)

5.5

d)

11/3

8.

Find the area under a curve defined by the equation 5x⁴+3x+7 between the x values 0 and 4.

a)

1200

b)

1/12

c)

1134

d)

1076

9.

Another word for 'integral' is .. .

a)

Constant

b)

Derivative

c)

Antiderivative

d)

Theorem

10.

Find the area under the curve y =3x²-2x from x= 1 to x =5.

a)

100

b)

99

c)

150

d)

152

11.

a)

a. 43

b)

b. 130/3

c)

c. 40

d)

d. 19/3

12.

a)

a. 24

b)

b. -8

c)

c. -10

d)

d. 22

13.

Find the Area under the curve.

a)

-500 ⁄ 3

b)

20 ⁄ 3

c)

500 ⁄ 3

d)

-20 ⁄ 3

14.

$\int_1^2\left(4-x\right)dx=$

a)

2.5

b)

$-\frac{5}{2}$

c)

$\frac{2}{5}$

d)

$-0.4$

15.

$\int_{-1}^1\left(2x-1\right)\left(2x+1\right)dx=$

a)

3

b)

$-\frac{2}{3}$

c)

$\frac{2}{3}$

d)

$-1.5$

16.

$\int_1^3\left(2-\frac{3}{x^2}\right)dx=$

a)

2

b)

$-\frac{1}{2}$

c)

$-2$

d)

$0.5$

17.

$\int_0^2\left(3x-1\right)^3dx=$

a)

52

b)

$25$

c)

$-5\frac{2}{5}$

d)

$\frac{5}{2}$

18.

$\int_1^2\frac{1}{\left(4x-3\right)^2}dx=$

a)

15

b)

$1.5$

c)

$-\frac{1}{5}$

d)

0.2

19.

$\int_1^2\left(2x+k\right)dx=8.$

$\ k=?$

a)

$4$

b)

$5$

c)

$-3$

d)

$-2$

20.

$\int_{-1}^a\left(-3x+4\right)dx=\frac{49}{8}.$

$\ a=?$

a)

$1$

b)

$2.5$

c)

$-3$

d)

$4$

21.

What is the value of the definite integral : $\int_{-3}^3x^2+x+1\ dx$ ?

a)

6

b)

9

c)

24

d)

33

22.

$\int_0^{\frac{\pi}{2}}\cos\left(x\right)\ dx$

a)

-1

b)

1

c)

$\pi$

d)

$\frac{\pi}{2}$

23.

$\int_0^3\left(3x^2-4x\right)dx=$

a)

9

b)

15

c)

16

d)

14

24.

$\int_1^4\ \left|x\ -\ 3\right|\ dx$ =

a)

$\frac{-5}{2}$

b)

6

c)

$\frac{-3}{2}$

d)

$\frac{5}{2}$

25.

$\int_{-2}^{-1}\ \left(4x^2\ +\ 3x\ -1\right)\ dx$ =

a)

$\frac{89}{6}$

b)

$\frac{23}{6}$

c)

7

d)

0

26.

$\int_1^3\left(2-\frac{3}{x^2}\right)dx=$

a)

2

b)

$-\frac{1}{2}$

c)

$-2$

d)

$0.5$

27.

$\int_0^2\left(3x-1\right)^3dx=$

a)

52

b)

$25$

c)

$-5\frac{2}{5}$

d)

$\frac{5}{2}$

28.

If $\int_2^5g\left(x\right)dx=12$ what is the average value of $g\left(x\right)$ on the interval $\left[2,5\right]$ ?

(a)

29.

For which functions below should we add 1 to the power to get an antiderivative?

a)

$f\left(x\right)=e^x$

b)

$f\left(x\right)=x^2$

c)

$f\left(x\right)=x^{-2}$

d)

$f\left(x\right)=x^{-1}$

e)

$f\left(x\right)=\sin x$

30.

Which integral has the largest value?

a)

$\int_a^bf\left(x\right)dx$

b)

$\int_b^cf\left(x\right)dx$

c)

$\int_a^cf\left(x\right)dx$

d)

$\int_a^df\left(x\right)dx$

31.

Find the average value of the function f(x) on the interval.

a)

A) (ln4) / 6

b)

B) (ln 14)/6

c)

C) -(ln 2) / 6

d)

D) 4(ln 2)/3

32.

$\int_0^1f\left(x\right)dx\$ is

a)

Positive

b)

Negative

c)

0

d)

Cannot be determined

33.

Which definite integral models the area highlighted above?

a)

b)

c)

d)

34.

Evaluate the definite integral.

a)

3

b)

9/2

c)

9

d)

Not possible

35.

a)

a. 43

b)

b. 130/3

c)

c. 40

d)

d. 19/3

36.

a)

8

b)

2

c)

4

d)

6

37.

Use the given function or the graph to find the average rate of change

a)

3

b)

-3

c)

3/2

d)

-1/3

38.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

39.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

40.

Find the average rate of change of f(x)=2x²+3x-1 from 1 to 2.

a)

18

b)

-9

c)

9

d)

3

Integration 2

Total questions: 40

Worksheet time: 3hrs 20mins

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