Free Printable AP Calculus 5.3 Review

1.

The area under a curve is calculated using which mathematical concept?

a)

antiderivative

b)

indefinite integral

c)

definite integral

d)

derivative

2.

The result of $\int_1^3\left(x-2\right)\ dx$ is:

a)

positive

b)

negative

c)

zero

3.

The result of $\int_0^2\left(x^2-2x+1\right)\ dx$ is:

a)

positive

b)

negative

c)

zero

4.

The result of $\int_0^2\left(x^3-2x^2-x+1\right)\ dx$ is:

a)

positive

b)

negative

c)

zero

5.

The shaded area in the figure is represented by which of the following integral expressions?

a)

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

b)

$-\int_2^{-1}f\left(x\right)\ dx$

c)

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

d)

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

6.

Which of the following is incorrect?

a)

$\int_b^af\left(x\right)\ dx=-\int_a^bf\left(x\right)\ dx$

b)

$\int_a^af\left(x\right)\ dx=0$

c)

$\int_a^bf\left(x\right)\ dx+\int_b^cf\left(x\right)\ dx$
$=\int_a^cf\left(x\right)\ dx$

d)

$\int_a^bf\left(x\right)\ dx-\int_b^cg\left(x\right)\ dx$
$=\int_a^c\left(f\left(x\right)-g\left(x\right)\right)\ dx$

e)

$\int_a^bf\left(x\right)\ dx-\int_a^bg\left(x\right)\ dx$
$=\int_a^b\left(f\left(x\right)-g\left(x\right)\right)\ dx$

7.

a)

2

b)

4

c)

1

d)

Not possible

8.

a)

-8

b)

8

c)

-2

d)

2

9.

Given the following integral values, find the integral below

a)

A

b)

B

c)

C

d)

D

10.

Given the following integral values, find the integral below

a)

A

b)

B

c)

C

d)

D

11.

Given the following integral values, find the integral below

a)

A

b)

B

c)

C

d)

D

12.

(a)

13.

If $\int_2^{10}f\left(x\right)dx=-6$
Find the value of $\int_{10}^2f\left(x\right)dx$

a)

- 6

b)

6

c)

2

d)

10

14.

If $\int_2^{10}f\left(x\right)dx=-6$
Find the value of $\int_2^{10}-2f\left(x\right)dx$

a)

- 12

b)

4

c)

- 8

d)

12

15.

If $\int_2^{10}f\left(x\right)dx=-6$
Find the value of $\int_2^{10}\ \frac{1}{3}f\left(x\right)dx$

a)

2

b)

18

c)

- 2

d)

- 18

16.

If $\int_0^2f\left(x\right)\ dx=5$ , $\int_2^4f\left(x\right)dx=3$ , and $\int_2^6\ f\left(x\right)dx\ =12$ , then $\int_0^6\ f\left(x\right)\ dx=$

a)

5

b)

-5

c)

17

d)

-17

17.

If a<c<b, answer the following:

a)

A

b)

B

c)

C

d)

D

e)

E

18.

If $\int_1^5f\left(x\right)dx=8$ , then $\int_2^2f\left(x\right)dx=$

a)

8

b)

-8

c)

0

d)

4

19.

$\int_{-a}^af\left(x\right)dx=$

a)

$0,\ if\ f\left(-x\right)=f\left(x\right)$

b)

$2\int_0^af\left(x\right),\ if\ f\left(-x\right)=f\left(x\right)$

c)

$2\int_0^af\left(x\right),\ if\ f\left(-x\right)=-f\left(x\right)$

d)

none of these

20.

$\int_{-3}^3\left|x+1\right|dx=$

a)

10

b)

0

c)

8

d)

none of these

AP Calculus 5.3 Review

Total questions: 20

Worksheet time: 16mins

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