Let R be the region bounded by y = 1/x, the x-axis, x = 1, and x = b, where b> 1. Let D be the solid formed when R is revolved about the x-axis. (a) Find the volume V of D. V = (b) Write a definite integral that represents the surface area S of D. S = 27 dx (c) Show that V approaches a finite limit as b-...

Let R be the region bounded by y = 1/x, the x-axis, x = 1, and x = b, where b> 1. Let D be the solid formed when R is revolved about the x-axis. (a) Find the volume V of D. V = (b) Write a definite integral that represents the surface area S of D. S = 27 dx (c) Show that V approaches a finite limit as b-...

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

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Question

Find volume of D and write definite integral SEE PHOTO

Let R be the region bounded by y = 1/x, the x-axis, x = 1, and x = b, where b> 1. Let D be the solid formed when R is revolved about the x-axis.
(a) Find the volume V of D.
V =
(b) Write a definite integral that represents the surface area S of D.
S = 27
dx
(c) Show that V approaches a finite limit as b - .

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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