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152review1Sp11 - Math 152 Spring 2011 Review for Midterm 1...

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Math 152, Spring 2011, Review for Midterm 1, sections 1–3, 7–9 Your first midterm examination is likely to contain some prob- lems that do not resemble these review problems. I. Applications of Integration (1-3) Find the volumes of the solids obtained by rotating the indicated region R in the xy -plane about the specified axis: (1) Region: R is bounded by y = 1, y = ln x and x = e 2 . Axes: ( a ) the line y = - 1; ( b ) the line x = - 2. (2) Region: R consists of all points ( x, y ) with 0 x π and 0 y sin x . Axes: (2 a ) the line y = - 2; (2 b ) the line x = - 1. (3) Region: R is bounded by x = y (4 - y ) and the y -axis Axis: the y -axis. (4) Write down the integral used to compute the work done against gravity in building a granite pyramid 500 feet high with a square base of side length 800 feet. Take the density of granite as 170 lbs per cubic foot. Explain in detail how the integral is obtained. (5) There is a point x 0 in the interval [5 , 7] where the function f ( x ) = ( x 2 - 4) - 1 / 2 takes on its average value over that interval.
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