P33Ans - every time x . concentration K ( x ) = 2( x-1) e x...

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Project 32/33 MAC 2233 1. Evaluate each of the following integrals using a basic substitution. Z 8 x 3 4 - 3 x 4 d x Z x 2 e - 2 x 3 d x each of these can be fairly easily by taking the derivative of your answer Z e 1 x 4 x 2 d x Z p 1 + 2 ln( x ) 4 x d x 2. Demonstrate that F ( u ) = ( u - 1) e u is an antiderivative for the function f ( u ) = ue u . take derivative of F Use the substitution u = x to relate the indefinite integral to f ( u ) , and use the formula above to calculate the indefinite integral: Z e x d x = 2( x - 1) e x + C Suppose the concentration of a chemical in the air changes at rate e x ppm/day, where x is the time elapsed in days. If there are 2 ppm initially, find a formula for the concentration at
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Unformatted text preview: every time x . concentration K ( x ) = 2( x-1) e x + 4 3. Over a four-hour period, the number of students within a certain campus building changes at a rate of ( x ) = 100 x 4-x , where x is the number of hours that have elapsed during that period. If the building is initially empty, how many students are present after 4 hours? number of students after x hours: N ( x ) = 40(4-x ) 5 2-800 3 (4-x ) 3 2 + 2560 3...
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