1 Name:__________________________________ Math 160 Section 002 Spring 2017 Written Assignment 8 Due at the start of class, Friday 7 April 2017 Instructions: Clearly show all work to receive full credit. Neatness counts. If asked, write a final sentence that gives your answer in the context of the question. Always include proper units when appropriate. Graphs should include properly labeled axes. Please do the work on separate paper. 1. Evaluate each definite integral. Show all work. Give exact answers. a) b) c) d) e) 2. ! 3 2 ! ! ! 3 ! ! ! ! !! ! ! ! ! ! !! The concentration of a certain drug, measured in mg/cm! , in a patient's bloodstream t hours after injection is = 0.2 +1 ! Write complete sentences, including proper units, to answer each of the following questions. a) What is the concentration when the drug is initially injected (t = 0)? b) What is the concentration of the drug after 6 hours (t = 6)? Round your answer to four decimal places. c) Determine the average concentration of the drug in the patient's bloodstream over the first 6 hours after the drug is injected. Round your answer to four decimal places. (Hint: this is not just the average of your answers to parts a) and b). It will require an integral.) 2 3. Follow the steps to find the area of the region completely enclosed by the graphs of these functions = ! + 4 = 2 3 a) Use a separate piece of graph paper or a graphing program to graph the two functions on the same coordinate axes. Use an appropriate scale to show the region completely enclosed by the two functions. Label the graphs. b) Set the functions equal to one another and solve for x to find the x-values of the points of intersection. c) Write the definite integral that will calculate the area enclosed between the graphs. d) Evaluate the integral to find the exact area enclosed by the graphs of the two functions