Exam 7: Additional Topics in Integration

The demand equation for the Sicard sports watch is given by where x (measured in units of a thousand) is the quantity demanded per week and p is the unit price in dollars.Use Simpson's Rule and (take n = 8) to estimate the consumer's surplus if the market price is $25/watch.(Round your answer to two decimal places)

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

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.

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. Hint: Use the formula . $ __________ thousand dollars.

Use the formula to find the integral.

Use the formula to find the integral.

Evaluate the following improper integral whenever it is convergent.

Find a bound on the error in approximating the given definite integral using the trapezoidal rule with n intervals. If necessary, round the answer to seven decimal places. Find a bound on the error in approximating the given definite integral using the Simpson's rule with n intervals. If necessary, round the answer to seven decimal places.

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval.