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SalasSV_10_07_ex

E find the lateral surface area of the solid in part c

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Unformatted text preview: d the x-axis, x ≥ 0. (a) Sketch . (b) Find the area of . (c) Find the volume of the solid obtained by revolving about the x-axis. (d) Find the volume obtained by revolving about the y-axis. (e) Find the lateral surface area of the solid in part (c). 46. What point would you call the centroid of the region in Exercise 45? Does Pappus’s theorem work in this instance? 47. Let be the region bounded by the curve y = e−x and the x-axis, x ≥ 0. (a) Show that has ﬁnite area. (The area is √ actually 1 π , as you will see in Chapter 16.) (b) Calculate 2 the volume generated by revolving about the y-axis. 48. Let be the region bounded below by y(x2 + 1) = x, above by xy = 1, and to the left by x = 1. (a) Find the area of . (b) Show that the solid generated by revolving about the x-axis has ﬁnite volume. (c) Calculate the volume generated by rev...
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