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Solve the problem by integration. -Find the volume generated by rotating the area bounded by Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln and Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln about the Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln


A) Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln π\pi ln Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln
B) Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln π\pi ln Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln
C) Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln π\pi ln Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln
D) Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln π\pi ln Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the A) \pi ln B) \pi ln C) \pi ln D) \pi ln

E) A) and D)
F) None of the above

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Give the appropriate form of the partial fraction decomposition. -Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) +


A) Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) + + Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) +
B) Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) + + Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) +
C) Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) + + Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) +
D) Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) + + Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) +

E) A) and B)
F) All of the above

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Evaluate the integral. - Evaluate the integral. - cos 8 \theta d \theta A) B) C) D) cos 8 θ\theta d θ\theta


A) Evaluate the integral. - cos 8 \theta d \theta A) B) C) D)
B) Evaluate the integral. - cos 8 \theta d \theta A) B) C) D)
C) Evaluate the integral. - cos 8 \theta d \theta A) B) C) D)
D) Evaluate the integral. - cos 8 \theta d \theta A) B) C) D)

E) C) and D)
F) A) and D)

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Solve the problem. -Consider the region R bounded by the graph of f(x) = Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis. A) \pi B) 2 \pi C) \pi D) 2 \pi on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis.


A) π\pi Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis. A) \pi B) 2 \pi C) \pi D) 2 \pi
B) 2 π\pi Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis. A) \pi B) 2 \pi C) \pi D) 2 \pi
C) π\pi Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis. A) \pi B) 2 \pi C) \pi D) 2 \pi
D) 2 π\pi Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis. A) \pi B) 2 \pi C) \pi D) 2 \pi

E) A) and C)
F) B) and C)

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Evaluate the integral by making a substitution and then using a table of integrals. -Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C


A) Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C + C
B) Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C + C
C) Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C + C
D) Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C Evaluate the integral by making a substitution and then using a table of integrals. - A) + C B) + C C) + C D) + C + C

E) B) and D)
F) B) and C)

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Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = on about the y-axis. Round to 3 decimal places. A) \pi \approx 8.268 B) \pi \approx 13.497 C) \pi \approx 12.021 D) \pi \approx 7.718 on Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = on about the y-axis. Round to 3 decimal places. A) \pi \approx 8.268 B) \pi \approx 13.497 C) \pi \approx 12.021 D) \pi \approx 7.718 about the y-axis. Round to 3 decimal places.


A) π\pi Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = on about the y-axis. Round to 3 decimal places. A) \pi \approx 8.268 B) \pi \approx 13.497 C) \pi \approx 12.021 D) \pi \approx 7.718 ≈\approx 8.268
B) π\pi Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = on about the y-axis. Round to 3 decimal places. A) \pi \approx 8.268 B) \pi \approx 13.497 C) \pi \approx 12.021 D) \pi \approx 7.718 ≈\approx 13.497
C) π\pi Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = on about the y-axis. Round to 3 decimal places. A) \pi \approx 8.268 B) \pi \approx 13.497 C) \pi \approx 12.021 D) \pi \approx 7.718 ≈\approx 12.021
D) π\pi Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = on about the y-axis. Round to 3 decimal places. A) \pi \approx 8.268 B) \pi \approx 13.497 C) \pi \approx 12.021 D) \pi \approx 7.718 ≈\approx 7.718

E) All of the above
F) A) and C)

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Solve the problem. -The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use Simpson's Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon. Solve the problem. -The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use Simpson's Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon. A) 9725 gal B) 8475 gal C) 7717 gal D) 8483 gal


A) 9725 gal
B) 8475 gal
C) 7717 gal
D) 8483 gal

E) A) and B)
F) A) and C)

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Express the integrand as a sum of partial fractions and evaluate the integral. -Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C


A) Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C + Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C ln Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C + C
B) Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C + Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C ln Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C + C
C) Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C + Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C ln Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C + C
D) Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C + Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C ln Express the integrand as a sum of partial fractions and evaluate the integral. - A) + ln + C B) + ln + C C) + ln + C D) + ln + C + C

E) A) and B)
F) A) and C)

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Integrate the function. -Integrate the function. - , x > 7 A) ln + C B) + C C) ln + C D) + C , x > 7


A) ln Integrate the function. - , x > 7 A) ln + C B) + C C) ln + C D) + C + C
B) Integrate the function. - , x > 7 A) ln + C B) + C C) ln + C D) + C + C
C) ln Integrate the function. - , x > 7 A) ln + C B) + C C) ln + C D) + C + C
D) Integrate the function. - , x > 7 A) ln + C B) + C C) ln + C D) + C + C

E) B) and C)
F) C) and D)

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Use Simpson's Rule with n = 4 steps to estimate the integral. -Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)


A) Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)
B) Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)
C) Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)
D) Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)

E) A) and B)
F) A) and C)

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Express the integrand as a sum of partial fractions and evaluate the integral. -Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) ln + C B) ln + C C) ln + C D) ln + C dx


A) ln Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) ln + C B) ln + C C) ln + C D) ln + C + C
B) ln Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) ln + C B) ln + C C) ln + C D) ln + C + C
C) ln Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) ln + C B) ln + C C) ln + C D) ln + C + C
D) ln Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) ln + C B) ln + C C) ln + C D) ln + C + C

E) A) and B)
F) A) and C)

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Use reduction formulas to evaluate the integral. -Use reduction formulas to evaluate the integral. - A) B) C) D)


A) Use reduction formulas to evaluate the integral. - A) B) C) D)
B) Use reduction formulas to evaluate the integral. - A) B) C) D)
C) Use reduction formulas to evaluate the integral. - A) B) C) D)
D) Use reduction formulas to evaluate the integral. - A) B) C) D)

E) B) and C)
F) A) and D)

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Evaluate the improper integral. -Evaluate the improper integral. - A) -16 B) 4 C) 16 D) -4


A) -16
B) 4
C) 16
D) -4

E) A) and B)
F) B) and D)

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Evaluate the integral. -Evaluate the integral. - A) B) C) D)


A) Evaluate the integral. - A) B) C) D)
B) Evaluate the integral. - A) B) C) D)
C) Evaluate the integral. - A) B) C) D)
D) Evaluate the integral. - A) B) C) D)

E) A) and C)
F) A) and D)

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Use integration by parts to establish a reduction formula for the integral. -Use integration by parts to establish a reduction formula for the integral. - A) B) C) D)


A) Use integration by parts to establish a reduction formula for the integral. - A) B) C) D)
B) Use integration by parts to establish a reduction formula for the integral. - A) B) C) D)
C) Use integration by parts to establish a reduction formula for the integral. - A) B) C) D)
D) Use integration by parts to establish a reduction formula for the integral. - A) B) C) D)

E) A) and B)
F) All of the above

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Use Simpson's Rule with n = 4 steps to estimate the integral. -Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)


A) Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)
B) Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)
C) Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)
D) Use Simpson's Rule with n = 4 steps to estimate the integral. - A) B) C) D)

E) B) and D)
F) A) and B)

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Evaluate the integral. -Evaluate the integral. - A) 2 + C B) 2 + C C) 2 + C D) 2 + C


A) 2 Evaluate the integral. - A) 2 + C B) 2 + C C) 2 + C D) 2 + C + C
B) 2 Evaluate the integral. - A) 2 + C B) 2 + C C) 2 + C D) 2 + C + C
C) 2 Evaluate the integral. - A) 2 + C B) 2 + C C) 2 + C D) 2 + C + C
D) 2 Evaluate the integral. - A) 2 + C B) 2 + C C) 2 + C D) 2 + C + C

E) C) and D)
F) B) and D)

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Express the integrand as a sum of partial fractions and evaluate the integral. - Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) B) C) D) dx


A) Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) B) C) D)
B) Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) B) C) D)
C) Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) B) C) D)
D) Express the integrand as a sum of partial fractions and evaluate the integral. - dx A) B) C) D)

E) A) and B)
F) A) and D)

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Find the volume. -Find the volume of the solid generated by revolving the region under the curve Find the volume. -Find the volume of the solid generated by revolving the region under the curve from to about the A) 9 \pi B) \pi C) 18 \pi D) 9 from Find the volume. -Find the volume of the solid generated by revolving the region under the curve from to about the A) 9 \pi B) \pi C) 18 \pi D) 9 to Find the volume. -Find the volume of the solid generated by revolving the region under the curve from to about the A) 9 \pi B) \pi C) 18 \pi D) 9 about the Find the volume. -Find the volume of the solid generated by revolving the region under the curve from to about the A) 9 \pi B) \pi C) 18 \pi D) 9


A) 9 π\pi
B) π\pi Find the volume. -Find the volume of the solid generated by revolving the region under the curve from to about the A) 9 \pi B) \pi C) 18 \pi D) 9
C) 18 π\pi
D) 9

E) A) and B)
F) A) and C)

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Evaluate the integral. -Evaluate the integral. - Give your answer in exact form. A) B) C) D) Give your answer in exact form.


A) Evaluate the integral. - Give your answer in exact form. A) B) C) D)
B) Evaluate the integral. - Give your answer in exact form. A) B) C) D)
C) Evaluate the integral. - Give your answer in exact form. A) B) C) D)
D) Evaluate the integral. - Give your answer in exact form. A) B) C) D)

E) A) and B)
F) A) and C)

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