Exam 7: Additional Topics in Integration

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

Find the indefinite integral.

The quantity demanded x (in thousands of pounds) of a certain brand of butter each week is a continuous random variable with probability density function What is the expected demand for this brand of butter each week?

Find the indefinite integral. Hint: First, make the substitution ; then, integrate by parts.

In using the trapezoidal rule, the number of subintervals n must be even.

The number of chocolate chips in each cookie of a certain brand has a distribution described by the probability density function Find the expected number of chips in each cookie.

Find the indefinite integral.

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

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

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

The life span of a certain plant species (in days) is described by the probability density function . Find the probability that a plant of this species will live more than 120 days.

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

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.

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 4 years from now? __________ people

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

Show that the function is a probability density function on the interval .

A university alumni group wishes to provide an annual scholarship in the amount of $1,300 beginning next year. If the scholarship fund will earn an interest rate of 8% / 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 curve over the indicated interval. __________ sq units

Find the indefinite integral.