Free Printable volume

1.

Find the area of the region enclosed by the lines and curves.
y = 3x + 4 and y = x² + 4

a)

9

b)

93/2

c)

9/2

d)

18

2.

Find the area between the x-axis and the curve y = x² - 5x

a)

125/6

b)

53,125/24

c)

5

d)

25/6

3.

Find the area under curve between a and b

a)

ln 2

b)

2 e²

c)

2ln2

d)

2e

4.

Find the area between the x-axis and y=x²-2x-12 from x=1 to 4

a)

-30

b)

-56

c)

30

d)

-128/3

5.

Find the area between the x-axis and y=x²-2x-12 from x=1 to 4

a)

-30

b)

-56

c)

30

d)

-128/3

6.

Write the integral that would be used to find the area bounded by y = x² + 1, y = x - 2, x = -2 and x = 2.

a)

b)

c)

d)

e)

7.

Write the integral that would be used to find the area of the region bounded by x = 1, y = √x and y = -x + 6.

a)

b)

c)

d)

e)

8.

Use the Disk method to find the volume of the solid obtained by revolving the shaded region about the y-axis.

a)

$Volume=\pi\int_0^2\ \left(\frac{3y}{2}\right)^2\ dy$

b)

$Volume=\pi\int_0^3\ \left(\frac{3y}{2}\right)^2\ dy$

c)

$Volume=\pi\int_0^3\ \left(\frac{2x}{3}\right)^2\ dx$

d)

$Volume=\pi\int_0^2\ \left(\frac{2x}{3}\right)^2\ dx$

9.

Select the integral that would find the volume of the region revolving around the given axis.

a)

b)

c)

d)

10.

What is the outer radius (R) needed to find the volume of the region revolving around $y=1$ ?

a)

$1-\left(-x^2+6\right)$

b)

$\left(-x^2+6\right)-1$

c)

$2-1$

d)

$1-2$

11.

What is the outer radius (R) needed to find the volume of the region revolving around $y=1$ ?

a)

$1-\left(-x^2+6\right)$

b)

$\left(-x^2+6\right)-1$

c)

$2-1$

d)

$1-2$

12.

Write the integral that would be used to find the volume of the region bounded by x = -1, x = 2, y = 0 and y = 1/2x² + 2.

a)

b)

c)

d)

e)

13.

For each problem, find the volume of the solid that results when the region enclosed by the curves is revolved about the y-axis. Set up, but do not evaluate the integral.

a)

A

b)

B

c)

C

d)

D

14.

Select the formula for finding area under a curve bounded by the x axis.

a)

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

b)

$\int_a^b\left[f\left(x\right)-g\left(x\right)\right]\ dx$

c)

$\int_a^b\left[f\left(x\right)\right]^2dx$

d)

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

15.

Find the integral for the area under the curve.

a)

$\int_{-6}^{-2}\ 2\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

b)

$\int_{-6}^{-2}\ -2\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

c)

$\int_{-6}^{-2}\ \left(x^2\ +\ 6x\ +\ 10\right)\ dx$

d)

$\int_{-6}^{-2}\ -4\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

volume

Total questions: 15

Worksheet time: 26mins

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