Free Printable Fundamental Theorem of Calculus (BPS)

1.

$\$ If F(x) = $\int_{-3}^x\sin xdx$ then F'(x) =

a)

cosx

b)

sin(-3)

c)

sinx

d)

$\sin\pi$

2.

$\$ Which of the following is equivalent to

\int_0^{\pi}\sin xdx

a)

$\int_0^{\pi}\cos xdx$

b)

$\int_{\pi}^{2\pi}\sin xdx$

c)

$\int_{-\pi}^0\sin xdx$

d)

$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sin xdx$

e)

$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\cos xdx$

3.

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

a)

-1/2

b)

7/24

c)

1/2

d)

1

e)

2ln2

4.

The graph of a piecewise linear function f for $-1\le x\le4$ is shown. What is the value of $\int_{-1}^4f\left(x\right)dx?$

a)

1

b)

4

c)

8

d)

2.5

e)

5.5

5.

$\$ If F(x) = $\int_0^x\left(\sqrt{t^3+1\ }\right)dt$ what is F'(2)

a)

-3

b)

-2

c)

2

d)

3

e)

18

6.

$\int_0^5e^{-x^2}dx$ Use your calculator to evaluate

a)

5

b)

0

c)

.443

d)

.886

e)

1

7.

$If\ \ \int_{-2}^5f\left(x\right)dx\ =\ -3\ \ \ \ \ \$ What is the value of $\int_5^{-2}f\left(x\right)dx\ =$

a)

-3

b)

0

c)

3

d)

7

8.

$\$ Find the area between y = -x and $y=x^2$ on [0,2]

a)

2/3

b)

8/3

c)

4

d)

14/3

e)

16/3

9.

$If\ \int_2^6f\left(x\right)dx=10$ then $\int_2^6\left(f\left(x\right)+5\right)dx=$

a)

15

b)

50

c)

30

d)

20

e)

10

10.

$\int_{\pi}^{2\pi}\theta d\theta=$

a)

$\pi^2$

b)

$\frac{3\pi^2}{2}$

c)

$3\pi^2$

d)

$6\pi^2$

11.

$What\ is\ the\ value\ of\ \sum_{n=0}^k\left(-1\right)^n\ if\ k\ is\ odd$

a)

0

b)

1

c)

-1

d)

3

12.

$\$ Find the average value of f(x)=2x on [1,5]

a)

12

b)

6

c)

24

d)

8

e)

10

13.

$\int_{\frac{1}{2}}^5\left(2-\frac{1}{\left(x\right)}\right)dx$

a)

9+ln10

b)

0

c)

5+ln(1/2)

d)

9-ln10

14.

$Find\ \ \ \int_{-4}^8\left|x\right|dx$ Using geometric formulas

a)

24

b)

0

c)

40

d)

-24

15.

$\ Approximate\ the\ value\ of\ \ \int_0^2xdx$ Using the Trapezoidal method where n=4

a)

2

b)

4

c)

8

d)

1

16.

$\ Evaluate\ \ \ \int_0^{10}\left(\frac{1}{\left(3+2\sin x\right)}\right)dx$ using your calculator

a)

12.324

b)

7.602

c)

3.802

d)

17.987

17.

$\$ Find the average value of y=sinx on the interval $\left[0,\pi\right]$

a)

$2\pi$

b)

$\pi$

c)

$\frac{2}{\pi}$

d)

$\frac{\pi}{2}$

18.

$\int_3^3\left(x^2+2x+1\right)\ dx$ =

a)

3

b)

0

c)

6

d)

-1

19.

$\$ If F(x)= $\int_0^xe^{-x^2}dx$ then F'(x)=

a)

$2xe^{-x^2}$

b)

$e^{-x^2}$

c)

$e^{-x^2}-1$

d)

$-2xe^{-x^2}$

20.

$\int_1^e\left(\frac{1}{x}\right)dx=$

a)

0

b)

-1

c)

1

d)

e

Fundamental Theorem of Calculus (BPS)

Total questions: 20

Worksheet time: 1hrs 26mins

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