This preview shows page 1. Sign up to view the full content.
Unformatted text preview: d the xaxis, x ≥ 0. (a) Sketch . (b) Find the area of . (c) Find the volume of the solid obtained by revolving about the xaxis. (d) Find the volume obtained by revolving about the yaxis. (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 xaxis, 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 yaxis. 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 xaxis has ﬁnite volume. (c) Calculate the volume generated by rev...
View
Full
Document
This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston  Downtown.
 Spring '10
 SMITH
 Improper Integrals, Integrals

Click to edit the document details