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AP Calculus BC Unit 8: Applications of Integration

12 questions

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Unit 8: Applications of Integration

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Question 1

The region bounded by $x = y^{2}$ and $x = 4$ is revolved around the $y$ -axis. Find the volume.

\frac{128 π}{5}

\frac{256 π}{5}

\frac{64 π}{3}

32 π

Question 2

Find the volume of the solid with a circular base of radius $2$ (centered at origin) and semicircular cross-sections perpendicular to the $x$ -axis.

\frac{16 π}{3}

\frac{32 π}{3}

8 π

\frac{8 π}{3}

Question 3

Find the volume of the solid formed by revolving the region between $y = x$ and $y = x$ on $[0, 1]$ around the $x$ -axis using the washer method.

\frac{π}{6}

\frac{π}{3}

\frac{π}{2}

\frac{π}{12}

Question 4

The region bounded by $x = y^{2}$ and $x = 4$ is revolved around the $y$ -axis. Find the volume.

\frac{128 π}{5}

16 π

\frac{64 π}{3}

32 π

Question 5

Find the area of the region bounded by $y = x^{2}$ and $y = 2 x$ .

\frac{4}{3}

\frac{8}{3}

2

\frac{2}{3}

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Question 6

A solid has a square cross-section perpendicular to the $x$ -axis, with the base region bounded by $y = cos x$ and $y = 0$ on $[- π /2, π /2]$ . Find the volume.

2

\frac{π}{2}

π

4

Question 7

Find the arc length of the curve $y = ln (cos x)$ on $[0, \frac{π}{4}]$ .

ln (2 + 1)

\frac{π}{4}

ln 2

sec (π /4) - sec (0)

Question 8

Find the volume of the solid formed by revolving $y = x$ on $[0, 4]$ around the $x$ -axis using the disk method.

4 π

8 π

16 π

\frac{32 π}{3}

Question 9

Find the volume of the solid generated by revolving $y = e^{x}$ on $[0, 1]$ around the $x$ -axis.

π (e^{2} - 1) /2

π (e - 1)

π e^{2}

2 π (e^{2} - 1)

Question 10

Find the arc length of $y = \frac{2}{3} x^{3/2}$ from $x = 0$ to $x = 3$ .

\frac{14}{3}

23

32

\frac{26}{3}

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Question 11

Find the average value of $f (x) = 2 x + 1$ on $[1, 4]$ .

4

6

9

3

Question 12

Find the volume of the solid generated by revolving the region bounded by $y = x^{2}$ and $y = x$ around the line $y = - 1$ using the washer method.

\frac{π}{2}

\frac{7 π}{15}

\frac{11 π}{15}

\frac{π}{15}

AP Calculus BC Unit 8: Applications of Integration — Free with Answer Explanations | Test Practice Hub