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Exam 7: Additional Topics in Integration

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Exam 1: Preliminaries183 Questionsadd course
Exam 2: Functions, Limits, and the Derivative250 Questionsadd course
Exam 3: Differentiation309 Questionsadd course
Exam 4: Applications of the Derivative152 Questionsadd course
Exam 5: Exponential and Logarithmic Functions256 Questionsadd course
Exam 6: Integration291 Questionsadd course
Exam 7: Additional Topics in Integration202 Questionsadd course
Exam 8: Calculus of Several Variables219 Questionsadd course
Exam 9: Differential Equations57 Questionsadd course
Exam 10: Probability and Calculus68 Questionsadd course
Exam 11: Taylor Polynomials and Infinite Series110 Questionsadd course
Exam 12: Trigonometric Functions64 Questionsadd course
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Find the indefinite integral. ​ Find the indefinite integral. ​ ​ ​

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Question 161

As a result of increasingly stiff laws aimed at reducing the number of alcohol-related traffic accidents in a certain state, preliminary data indicate that the number of such accidents has been changing at the rate of ​ As a result of increasingly stiff laws aimed at reducing the number of alcohol-related traffic accidents in a certain state, preliminary data indicate that the number of such accidents has been changing at the rate of ​ ​ Accidents/month t months after the laws took effect. There were 962 alcohol-related accidents for the year before the enactment of the laws. Determine how many alcohol-related accidents were expected during the first year the laws were in effect. Please round the answer to the nearest integer. ​ ​ Accidents/month t months after the laws took effect. There were 962 alcohol-related accidents for the year before the enactment of the laws. Determine how many alcohol-related accidents were expected during the first year the laws were in effect. Please round the answer to the nearest integer. ​

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Question 162

Find the volume of the solid of revolution obtained by revolving the region under the curve ​ Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. ​ from Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. to Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. about the Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. -axis.

(Short Answer)
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Question 163

In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​ In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​ In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​ In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​ In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​ In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​ In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​ In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. Time, t (hr) 0 Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​ Velocity, V(t) (mph) 19)4 23 33)8 39)4 37)2 35)1 27)8 26)2 3)8 ​

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Question 164

The membership of the Cambridge Community Health Plan (a health maintenance organization) is projected to grow at the rate of The membership of the Cambridge Community Health Plan (a health maintenance organization) is projected to grow at the rate of thousand people/year, t years from now. If the HMO's current membership is 30,000, what will the membership be 4 years from now? ​ __________ people thousand people/year, t years from now. If the HMO's current membership is 30,000, what will the membership be 4 years from now? ​ __________ people

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Question 165

Sales of the latest recording by Brittania, a British rock group, are currently Sales of the latest recording by Brittania, a British rock group, are currently units/week (each unit representing 10,000 discs), where t denotes the number of weeks since the recording's release. Find an expression that gives the total number of discs sold as a function of t. units/week (each unit representing 10,000 discs), where t denotes the number of weeks since the recording's release. Find an expression that gives the total number of discs sold as a function of t.

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Question 166

The membership of the Cambridge Community Health Plan (a health maintenance organization) is projected to grow at the rate of The membership of the Cambridge Community Health Plan (a health maintenance organization) is projected to grow at the rate of thousand people/year, t years from now. If the HMO's current membership is 40,000, what will the membership be 3 years from now? ​ thousand people/year, t years from now. If the HMO's current membership is 40,000, what will the membership be 3 years from now? ​

(Multiple Choice)
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Question 167

Evaluate the following improper integral whenever it is convergent. ​ Evaluate the following improper integral whenever it is convergent. ​ ​ ​

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Question 168

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-ft intervals. Using Simpson's rule with A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-ft intervals. Using Simpson's rule with , estimate the surface area of the lake. Round the result to the nearest tenth. ​ ​ , estimate the surface area of the lake. Round the result to the nearest tenth. ​ A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-ft intervals. Using Simpson's rule with , estimate the surface area of the lake. Round the result to the nearest tenth. ​ ​ ​

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Question 169

Find the volume of the solid of revolution obtained by revolving the region under the curve ​ Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. ​ from Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. to Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. about the Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. -axis.

(Short Answer)
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Question 170

Evaluate the definite integral by using the method of integration by parts. ​ Evaluate the definite integral by using the method of integration by parts. ​

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Question 171

Find the area of the region under the given curve Find the area of the region under the given curve over the indicated interval. ​ over the indicated interval. ​ Find the area of the region under the given curve over the indicated interval. ​

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Question 172

Find the volume of the solid of revolution obtained by revolving the region under the curve ​ Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. ​ from Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. to Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. about the Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. -axis.

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Question 173

Find the area of the region under the graph of Find the area of the region under the graph of from to . ​ from Find the area of the region under the graph of from to . ​ to Find the area of the region under the graph of from to . ​ . ​

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Question 174

Find the volume of the solid of revolution obtained by revolving the region bounded by the graphs of the given functions about the x-axis. ​ Find the volume of the solid of revolution obtained by revolving the region bounded by the graphs of the given functions about the x-axis. ​ and and Find the volume of the solid of revolution obtained by revolving the region bounded by the graphs of the given functions about the x-axis. ​ and

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Question 175

Use the table of integrals to find the integral. ​ Use the table of integrals to find the integral. ​ ​ ​

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Question 176

Use the table of integrals to find the integral. ​ Use the table of integrals to find the integral. ​ ​ ​

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Question 177

Find the volume of the solid of revolution obtained by revolving the region under the curve ​ Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. ​ from Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. to Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. about the Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis. -axis.

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Question 178

Evaluate the definite integral by using the method of integration by parts. ​ Evaluate the definite integral by using the method of integration by parts. ​ ​ ​

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Question 179

Use the formula ​ Use the formula ​ ​ To find the integral. ​ ​ ​ To find the integral. ​ Use the formula ​ ​ To find the integral. ​ ​ ​

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Question 180
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