Exam 6: Antiderivatives and Applications

Use integration by parts to find . (Give the exact answer in terms of natural logs.)

Evaluate .

The following figure is a graph of . On which of the following intervals is f decreasing?

Use integration by parts to find .

Fuel pressure in the fuel tanks of the space shuttle is decreasing at a rate of psi per second at time t in seconds. By how many total psi has the pressure decreased during the first minute? Round to 2 decimal places.

Evaluate .

Your company is downsizing and offers you a bonus if you retire early. You have a choice between a lump sum of $52,000 now or an income stream of $6200 per year for 10 years. You plan to use the money for a trip around the world in 10 years. You can earn interest at a continuous rate of 4%. Which option would be the better choice, and how much will you have for your trip?

Use the Fundamental Theorem of Calculus to determine the value of b if the area under the graph of between and is 8. Assume .

Calculate .

Given the values of in the table and that , estimate to the nearest whole number.

Supply and demand curves for a product are given by the equations Demand: Supply: where p is price in dollars and q is quantity. Compute the producer surplus. Round to the nearest cent.

A consultant expects an income stream of $15,000 per year for the next 8 years. A. Find the present value of this income stream if the interest rate is 2% per year, compounded continuously. B. Find the future value of this income stream under the same conditions.

What is the present value of an income stream of $1000 per year for 10 years with an annual interest rate of 10%, compounded continuously? Round to the nearest dollar.

The supply and demand curves for a product have equations and , respectively, with equilibrium at . Which of the following is a formula for total gains from trade?

Find .

Suppose and . Find the value of .

Suppose and . Estimate the value of to 4 decimal places.

The following figure shows the demand and supply curves for a product. Estimate the total gains from trade.

The graph of the derivative F' of a function F is shown. Assuming that F(20) = 10, estimate the maximum value attained by F.

, where a is a constant.