Exam 7: Additional Topics in Integration

Tracy purchased a 15-year franchise for a computer outlet store that is expected to generate income at the rate of ​ ​ dollars/year. If the prevailing interest rate is 10% /year compounded continuously, find the present value of the franchise.

Evaluate the improper integral whenever it is convergent. ​ ​

Approximate the value of the definite integral. ​ ​ Use the trapezoidal rule. Please give the answer to four decimal places. ​ Use the Simpson's rule. Please give the answer to four decimal places.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral. ​ ​

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

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

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

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

Find a bound on the error in approximating the given definite integral using (a) the trapezoidal rule and (b) Simpson's rule with n intervals. ​ ​

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

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

Thanks to smaller and more fuel-efficient models, American carmakers have doubled their average fuel economy over a 13-year period, from 1974 to 1987. The graph depicted in the figure gives the average fuel consumption in miles per gallon (mpg) of domestic-built cars over the period under consideration ( corresponds to the beginning of 1974). Use the trapezoidal rule to estimate the average fuel consumption of the domestic car built during this period. Round the result to the nearest hundredth. (Hint: Approximate the integral ​ ) Please round your answer to two decimal places. __________ mpg

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. Please give the answer to four decimal places. ​ ​ Trapezoidal rule: __________ ​ Simpson's rule: __________ ​ Exact value: __________

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

Tracy purchased a 15-year franchise for a computer outlet store that is expected to generate income at the rate of ​ ​ Dollars/year. If the prevailing interest rate is 10% /year compounded continuously, find the present value of the franchise. (Hint: Use the formula of the present value .) Please round the answer to the nearest cent.

Find the indefinite integral. ​

If f is a polynomial function of degree more than 3, then the approximation using Simpson's rule is exact. ​

If exists, then exists and .

In a study conducted by a certain country's Economic Development Board regarding the income distribution of certain segments of the country's workforce, it was found that the Lorentz curve for the distribution of income of college professors is described by the function ​ ​ Compute the coefficient of inequality of the Lorentz curve. Round to two decimal places. ​