Exam 7: Additional Topics in Integration

The number of voters in a certain district of a city is expected to grow at the rate of people per year years from now. If the number of voters at present is , how many voters will be in the district years from now? Please round your answer to the nearest integer. __________ people

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

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.

The demand function for Apex women's boots is where p is the wholesale unit price in dollars and x is the quantity demanded daily, in units of a hundred. Find the consumers' surplus if the wholesale price is set at $50/pair.

Determine whether the statement is true or false. If f is a polynomial function of degree less than or equal to 3, then the approximation using Simpson's rule is exact.

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

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

Evaluate the following improper integral whenever it is convergent.

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.

Evaluate the following improper integral whenever it is convergent.

Find the area of the region bounded by the x-axis and the graph of the function. __________ sq units

Use the formula to find the integral.

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.

As a result of increasingly stiff laws aimed at reducing the number of alcohol-related traffic accidents in a certain state, preliminary data indicate that the number of such accidents has been changing at the rate of accidents/month t months after the laws took effect. There were 982 alcohol-related accidents for the year before the enactment of the laws. Determine how many alcohol-related accidents were expected during the first year the laws were in effect. Please round the answer to the nearest integer.

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

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

Find a bound on the error in approximating the definite integral Please round your answers to seven decimal places. Using the trapezoidal rule with 6 intervals. Using Simpson's rule with 6 intervals.

Evaluate the following improper integral whenever it is convergent.

Use the table of integrals to find the given integral.

The present value of a perpetual stream of income that flows continually at the rate of dollars per year is given by the formula where is the interest rate compounded continuously. Using this formula, find the present value of a perpetual net income stream that is generated at the rate of dollars per year. Hint: .