Exam 7: Additional Topics in Integration

Find the indefinite integral.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Please give the answer to four decimal places. Trapezoidal rule: __________ Simpson's rule: __________

Use the table of integrals to find the integral.

Evaluate the following improper integral whenever it is convergent.

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

Find the area of the region bounded by the x-axis and the graph of the function

Evaluate the following improper integral whenever it is convergent.

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

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

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 60,000, what will the membership be 3 years from now?

Find the indefinite integral. Hint: Integrate by parts twice.

Determine whether the given function is a probability density function on the specified interval.

A university alumni group wishes to provide an annual scholarship in the amount of $1,800 beginning next year.If the scholarship fund will earn an interest rate of 9% / year compounded continuously, find the amount of the endowment the alumni are required to make now.

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

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

The management of AstroWorld ("The Amusement Park of the Future") estimates that the number of visitors (in thousands) entering the amusement park t hours after opening time at 8 A.M.is given by per hour.Determine the number of visitors admitted by noon.Round to the nearest integer.__________ visitors 23,570

Evaluate the following improper integral whenever it is convergent.

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 .)

Determine whether the statement is true or false. In using the trapezoidal rule, the number of subintervals n must be even.

Use the table of integrals to find the integral.