Use the shell method to set up and evaluate the integral that gives the volume of the solid...
Question:
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by {eq}y = \frac{1}{x}, x=7,x=8 {/eq} about the x-axis.
Volume of the Region:
The region is being revolved around the x=axis thus we can use the disc method to compute the volume of the solid formed revolution. This means that the we use the formula
{eq}V=\pi \int_{a}^{b}r^{2}h {/eq} where {eq}r {/eq} is the radius and {eq}h {/eq} is the height.
Answer and Explanation: 1
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From the graph,
{eq}r=y,\:h=dx {/eq}
Substituting to the formula {eq}V=\pi \int_{a}^{b}r^{2}h {/eq}
Thus,
{eq}\d...
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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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