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.(Hint: Use the formula of the present value .) Please round the answer to the nearest cent.

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

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 the Trapezoidal Rule (take n = 8) to estimate the consumers' surplus if the market price is $25/watch.Round answer to two 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.

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.

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

Use the table of integrals to find the integral.

Use the formula to find the integral.

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

The commissioner of the City of Newton Department of Public Works estimates that the number of people in the city who have been recycling their magazines in year t following the introduction of the recycling program at the beginning of 1990 is Find the average number of people who will have recycled their magazines during the first 3 years since the program was introduced.

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 amount of snowfall in feet in a remote region of Alaska in the month of January is a continuous random variable with probability density function Find the amount of snowfall one can expect in any given month of January in Alaska. __________ ft

The amount of snowfall in feet in a remote region of Alaska in the month of January is a continuous random variable with probability density function Find the amount of snowfall one can expect in any given month of January in Alaska.

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

Find the indefinite integral.

In using Simpson's rule, the number of subintervals n may be chosen to be even.

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure.The measurements shown were taken at 10-foot intervals.Using Simpson's rule with , estimate the surface area of the lake.Round the result to the nearest tenth. __________

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

Evaluate the definite integral by using the method of integration by parts.

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