1. Consider the finite region R bounded by the curves x 2y? +1 and the curve x = y² +2. (a) Sketch a picture of the solid of revolution obtained by revolving R around the y-axis. In your sketch, draw and label a representative slice of the solid. (b) Give an expression for the volume of a representative slice. (c) Using your answer from the previous part write a definite integral whose value is the exact volume of the solid. (You do not need to evaluate the expression.)

1. Consider the finite region R bounded by the curves x 2y? +1 and the curve x = y² +2. (a) Sketch a picture of the solid of revolution obtained by revolving R around the y-axis. In your sketch, draw and label a representative slice of the solid. (b) Give an expression for the volume of a representative slice. (c) Using your answer from the previous part write a definite integral whose value is the exact volume of the solid. (You do not need to evaluate the expression.)

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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