Exam 7: Additional Topics in Integration

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.

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.

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.

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

Find the indefinite integral.

Evaluate the following improper integral whenever it is convergent.

Find the function f given that the slope of the tangent line to the graph of f at any point and that the graph passes through the point (0, 3).

Use the formula to find the integral.

Determine whether the statement is true or false. If exists, then exists and .

The amount of time t (in seconds) it takes a motorist to react to a road emergency is a continuous random variable with probability density function What is the expected reaction time for a motorist chosen at random?

Find the indefinite integral.

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

Use the table of integrals to find the integral.

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

Use the table of integrals to find the integral.

Find the indefinite integral.

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

Evaluate the following improper integral whenever it is convergent.