Use the Shell Method to compute the volume of the solid obtained by rotating the region enclosed...
Question:
Use the Shell Method to compute the volume of the solid obtained by rotating the region enclosed by the graphs of the functions: {eq}y = x^2, \; y = 8 - x^2, {/eq} and to the right of {eq}x = 0 {/eq} about the {eq}y {/eq}-axis.
Volume of Solid of Revolution:
To calculate the volume of the solid formed by revolving the region around y-axis we will use the cylindrical shell method which has the formula
{eq}V=2\pi \int_{a}^{b}rh\:dr {/eq} where {eq}r {/eq} is the centroid of the region, {eq}h {/eq} for the height and {eq}dr {/eq} for the width.
Answer and Explanation: 1
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View this answerBelow is the graph,
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From the graph,
{eq}r=x,\:h=y,\:dr=dx {/eq}
Thus,
{eq}V=2\pi \int_{a}^{b}xydx {/eq}
{eq}V=2\pi...
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How to Find Volumes of Revolution With Integration
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Chapter 14 / Lesson 5
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The volume of a revolution can be calculated using the slicing method, the disk method, and the washer method. Explore the processes of the three methods and discover how to use them to find the volumes of revolution.
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