Exam 13: Definite Integrals - Techniques

A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by where x is in hours and . Find the average number of milligrams of the drug in the bloodstream for the first 3 hours after a capsule is taken. Round your answer to the nearest milligram. ​

Suppose the Gini coefficient of income for a certain country is If the Lorenz curve for this country is , find the value of p. ​

Use an integral formula to evaluate . ​

For what value of c does ? ​

Use Simpson's Rule to approximate with n = 4. Round your answer to 2 decimal places. ​

Suppose the number of daily sales of a product was found to be given by , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from to . Round your answer to the nearest dollar. ​

Use Simpson's Rule to approximate with n = 6. Round your answer to 3 decimal places. ​

Find the value of the given sum and round to four decimal places. ​ ​

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place. ​

Use an integral formula to evaluate . ​

Use rectangles to find the area between and the x-axis from to ​

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables. ​

Use integration by parts to evaluate . Note that evaluation may require integration by parts more than once. ​

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year. ​

Suppose the Lorenz curve for the distribution of income of a certain country is given by Find the Gini coefficient of income. Round your answer to three decimal places. ​

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. ​ I. Integration by parts II. III. IV.

Evaluate the definite integral . ​

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years. ​

Use Simpson's Rule to approximate with n = 6. Round your answer to two decimal places. ​

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to the nearest dollar. ​