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Unformatted text preview: Project 33 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. Examine the function f ( x ) = x 2- x + 2 x on ( 0 , ∞ ) . Find any one antiderivative for f ( x ). What is the general antiderivative for f ( x ) ? Calculate the indefinite integral Z f ( x ) d x . Calculate the exact area under f ( x ) on [ 1 , 2 ] . Note: justify that the func- tion is always positive on the interval using quadratic formula. Suppose the rate (in liters per hour) at which water runs into a trough during a rainstorm is given by f ( t ), where t represents the time in hours after the rainstorm begins. What is the exact change in the volume of water in the trough between the fourth and eighth hours of the storm? Combine any logarithms contained in your answer into a single logarithm. If the trough contains 20 liters at the start of the first hour, find the function V ( t ) that represents the amount of water in the tank after t hours....
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