Exam 7: Additional Topics in Integration

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 three 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 five decimal places.

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

The supply function for the CD manufactured by Herald Records is given by where p is the unit price in dollars and x stands for the quantity that will be made available in the market by the supplier, measured in units of a thousand. Use Trapezoidal Rule (take n = 8) to estimate the producers'surplus if the price is $8/CD. Round answer to two decimal places.

The number of streets in the downtown section of a certain city that need repairs in a given year is a random variable with a distribution described by the probability density function Find the probability that at most half of the streets will need repairs in any given year.

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

Suppose the time intervals between arrivals of successive cars at an expressway tollbooth during rush hour are exponentially distributed and that the average time interval between arrivals is 8 seconds. Find the probability that the average time interval between arrivals of successive cars is more than 8 seconds. Round your answer to two decimal places.

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 .

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.

Use the table of integrals to find the integral. Hint: First use the substitution u = x + 5.

Use the table of integrals to find the integral.

Use the table of integrals to find the integral.

Find a bound on the error in approximating the given definite integral using (a) the trapezoidal rule and (b) Simpson's rule with n intervals.

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

Thanks to smaller and more fuel-efficient models, American carmakers have doubled their average fuel economy over a 13-year period, from 1974 to 1987. The graph depicted in the figure gives the average fuel consumption in miles per gallon (mpg) of domestic-built cars over the period under consideration ( corresponds to the beginning of 1974). Use the trapezoidal rule to estimate the average fuel consumption of the domestic car built during this period. Round the result to the nearest hundredth. (Hint: Approximate the integral .)

Use the formula to find the integral.

In a submerged trial run of an attack submarine, a reading of the sub's velocity was made every quarter hour, as shown in the accompanying table. Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period. Please round the answer to the nearest hundredth if necessary. __________ miles

Find the indefinite integral.

Find the indefinite integral.

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