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6RevWksht S09

# 6RevWksht S09 - Review for Chapter 6 1 Let the base of a...

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Review for Chapter 6 1. Let the base of a solid be a 30 o - 60 o right triangle, with smallest leg of length 3 units. The cross sections of the solid perpendicular to that leg are semicircles. Draw a picture of the base, and a cross section, and then find the volume V of the solid. 2. Let f ( x ) = 3 x - x 2 , and let R denote the region bounded by the graph of f and the x axis. Calculate the volume V 1 of the solid generated by revolving R about the x axis, and draw an associated figure of the solid. Then calculate the volume V 2 of the solid generated by revolving R about the y axis, and draw an associated figure of the solid. From your figures, would you guess which of the volumes, V 1 or V 2 , should be the larger? 3. Let f ( x ) = x 5 + c/x 3 , for 1 x 2. We wish to find the length L of the graph of f . Determine a positive value of c for which you can evaluate the integral that arises. Then find the value of L . 4. Suppose that when a spring is extended 6 centimeters the work W done is 38 ergs. How much work W 0 is done in bringing it back to its natural length?
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