Exam 7: Additional Topics in Integration

Simpson's rule is more accurate than the trapezoidal rule. ​

Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph passes through the point (0, 6). ​

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

In a submerged trial run of an attack submarine, a reading of the sub'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) 17.5 20.6 26.8 31 29.6 27.3 18.8 16.3 5.6 ​ __________ miles

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

Evaluate the following improper integral whenever it is convergent. ​

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

Evaluate the following improper integral whenever it is convergent. ​

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 ​

The number of voters in a certain district of a city is expected to grow at the rate of ​ ​ people per year t years from now. If the number of voters at present is 20,000, how many voters will be in the district 6 years from now? Please round your answer to the nearest integer. __________ people

Find the indefinite integral. ​

Find the area of the region under the curve over the indicated interval. ​ ​ __________ sq units

Becky Wilkinson wants to establish a trust fund that will provide her children and heirs with a perpetual annuity in the amount of ​ ​ thousand dollars per year beginning next year. If the trust fund will earn an interest rate of 10% per year compounded continuously, find the amount that she must place in the trust fund now. ​

The number of voters in a certain district of a city is expected to grow at the rate of ​ ​ People per year t years from now. If the number of voters at present is 30,000, how many voters will be in the district 5 years from now? ​

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve ​ ​ and below by the curve ​ ​ from to about the -axis.

Find the indefinite integral. ​ ​

Use the table of integrals to find the integral. ​ ​ Use C as the constant of integration.

Evaluate the following improper integral whenever it is convergent. ​ ​ Enter divergent if the integral is divergent.

Evaluate the improper integral whenever it is convergent. If not, enter divergent. ​

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