Exam 6: Techniques of Integration

A body assimilates a 16-hour cold tablet at a rate modeled by , where C is measured in milligrams and t is the time in hours.Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 16 hours.

​Identify u and dv for finding the integral using integration by parts. ​ ​

Use integration by parts to evaluate ​. ​

Use a table of integrals with forms involving to find ​

​Use a table of integrals to find the indefinite integral ​

​Evaluate the improper integral if it converges,or state that it diverges. ​ ​

​Use a table of integrals to find the indefinite integral ​

​Decide whether the integral is proper or improper. ​ ​

Find the indefinite integral. ​ ​

Find the indefinite integral. ​. ​

​Evaluate the definite integral Round your answer to three decimal places. ​

​Use a table of integrals with forms involving to find the integral. ​ ​ ​

Use a table of integrals to find the indefinite integral ​

​Evaluate the definite integral Round your answer to three decimal places. ​

​A business is expected to yield a continuous flow of profit at the rate of $200,000 per year.If money will earn interest at the nominal rate of 2% per year compounded continuously,what is the present value of the business forever? ​

Find the indefinite integral. ​ ​ ​

​Evaluate the improper integral if it converges,or state that it diverges. ​ ​

Use the Trapezoidal Rule to approximate the value of the definite integral , Round your answer to three decimal places. ​

A model for the ability M of a child to memorize,measured on a scale from 0 to 10,is , where t is the child's age in years.Find the average value predicted by the model for a child's ability to memorize between second and third birthdays.Round your answer to three decimal places.

​Find the indefinite integral. ​ ​ ​