Answered: Use the method of cylindrical shells to…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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I am having a problem finding the correct answer to this problem. I have tried interpreting for y using the cylindrical method and got 2pie as well as 16pie/15 as an answer which both were wrong. I don't know what I'm doing wrong.

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
x = 4y2, y > 0, x = 4; about y = 2

Expert Solution

Step 1:Introduction

Volume by cylindrical shells $v = \int_{a}^{b} 2 πxf (x) d x$

where, x = radius of the cylinder, f(x) = height of the cylinder

dx = thickness of the cylinder shells

a,b limits of the height

given the region bounded by the curves.

$x = 4 y^{2}, y ⩾ 0, x = 4; a b o u t y = 2$

since the rotation of the curve is around the x-axis(parallel to). The volume will be horizontal in nature.

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