Free Printable Area and Volume (Calculus)

1.

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)

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

2.

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)

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

3.

Find the integral that would find the area of the region enclosed by the curves.

a)

$\int_0^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx$

b)

$\int_1^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx$

c)

$\int_1^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx$

d)

$\int_0^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx$

4.

Select the formula(s) for find the volume of a solid of revolution around an axis using the disk method.

a)

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

b)

$\pi\int_a^b\ f\left(y\right)^2\ dy$

c)

$\pi\int_a^b\ f\left(x\right)^{ }dx$

d)

$\pi\int_a^b\ \ R\ dx$

5.

Select the formula(s) to find the volume of a solid of revolution using the washer method.

a)

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

b)

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

c)

$\pi\int_a^b\left[R^2-r^2\right]dx$

d)

$\pi\int_a^b\left[f\left(y\right)^2-g\left(y\right)^2\right]dy$

6.

If the region from (-1,0) is rotated about the x axis, would one use a washer or disk?

a)

washer

b)

disk

7.

If the region enclosed by these functions are revolved around the y axis, would one use a washer or disk?

a)

washer

b)

disk

8.

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)

$1-2$

9.

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

a)

b)

c)

d)

10.

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

a)

b)

c)

d)

11.

Find the area of the region

a)

b)

c)

d)

12.

Find the volume of the solid formed when cross sections perpendicular to the x axis are squares

a)

b)

c)

d)

13.

Find the volume of the solid formed when cross sections perpendicular to the x axis are semi-circles

a)

b)

c)

d)

14.

The region bounded by the line y = x and y = f(x) is rotated about the line y = k. Choose the correct representations of R and r

a)

R = k + f(x)

b)

R = k − f(x)

c)

r = k + x

d)

r = k − x

15.

The shaded region is bound by y = 2x, y = -2x, and y = x + 3. Choose two integrals that can be added to find the area of the shaded region.

a)

$\int_{-1}^0\ \left(x+3-2x\right)dx$

b)

$\int_{-1}^0\left(x\ +\ 3\ +\ 2x\right)dx$

c)

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

d)

$\int_0^3\left(x+3\ +\ 2x\right)dx$

Area and Volume (Calculus)

Total questions: 15

Worksheet time: 17mins

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