Review for Chapter 61. Let the base of a solid be a 30o-60oright triangle, with smallest leg of length 3 units. The crosssections of the solid perpendicular to that leg are semicircles. Draw a picture of the base, and a crosssection, and then find the volumeVof the solid.2. Letf(x) = 3x-x2, and letRdenote the region bounded by the graph offand thexaxis. Calculatethe volumeV1of the solid generated by revolvingRabout thexaxis, and draw an associated figureof the solid. Then calculate the volumeV2of the solid generated by revolvingRabout theyaxis,and draw an associated figure of the solid. From your figures, would you guess which of the volumes,V1orV2, should be the larger?3. Letf(x) =x5+c/x3, for 1≤x≤2. We wish to find the lengthLof the graph off. Determine apositive value ofcfor which you can evaluate the integral that arises. Then find the value ofL.4. Suppose that when a spring is extended 6 centimeters the workWdone is 38 ergs. How much workW0is done in bringing it back to its natural length?
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Right triangle, United States customary units, Let, natural length, smallest leg