Use the Shells Method to set up (do not evaluate) an integral for the volume of the solid...
Question:
Use the Shells Method to set up (do not evaluate) an integral for the volume of the solid obtained by rotating the region enclosed by {eq}y = 4x - x^2 {/eq} and y = 0 about the y-axis.
Volume of Solid of Revolution:
Since using the cylindrical shell method thus the formula to use is {eq}V=2\pi \int_{a}^{b}rh\:dr {/eq} where {eq}r {/eq} is the centroid of the region, {eq}h {/eq} is the height and {eq}dr {/eq} is the width. The limits of integration are the intersections between the given equations.
Answer and Explanation: 1
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From the graph,
{eq}r=x,\:h=y,\:dr=dx {/eq}
Substituting to the formula {eq}V=2\pi \int_{a}^{b}rh\:dr {/eq}
Thus,...
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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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