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Unformatted text preview: Exam 4 Review MAC 2233 * This is intended to help you review some of the material that could appear on the exam. It is not inclusive of all topics discussed in lecture. 1. Evaluate the following integrals: Z ( x + 1 ) 2 x d x Z x ( x 2- 4) 3 d x Z x (2- x ) 10 d x Z e 2 1 [ 1 + 2 ln( x ) ] 2 x d x Z e 2 x ( e 2 x + e ) 5 d x Z 5 | 9- x 2 | d x Z 2 x e 1- x 2 d x Z x 2 4- x d x Z 3 x 1 + x 2 d x 2. Which indefinite integral below is easily done by substitution? Calculate it. (a) Z x 2 (2 x 3 + 1) 10 d x (b) Z x (2 x 3 + 1) 10 d x How could the other one be done? (Do not calculate, just explain.) 3. Approximate the area on [ 1 , 3 ] that is bounded by the x-axis and the curve y = x 4 x by using a Riemann Sum with 4 subintervals of equal width and x i = right endpoint. 4. Suppose the number of Americans employed by foreign companies (in millions) is expected to change at a rate given by the formula A ( x ) = 10 x- 1 ( 1 + ln( x ) )- 1 , where x is the number of years from the present. Find the net change in employment by foreign companies over theof years from the present....
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