Find the volume V of the solid obtained by rotating the region bounded by the curves y =...

Question:

Find the volume V of the solid obtained by rotating the region bounded by the curves {eq}y = \displaystyle\frac{7}{x}, x = 1, x = 4, y = 0 {/eq} about the x-axis.

Calculating Volume using the Disk Method:

A solid of revolution can be generated by graphing the function {eq}y = f(x) \geq 0 {/eq} on the interval {eq}a \leq x \leq b, {/eq} then revolving the graph around the {eq}x {/eq} axis. The volume is

{eq}V = \pi \displaystyle\int_a^b (f(x))^2 \: dx. {/eq}

Answer and Explanation:

We can calculate this volume using the Disk Method:

{eq}\begin{eqnarray*}V & = & \pi \int_1^4 \left( \displaystyle\frac{7}{x} \right)^2 \: dx \\ &...

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Disk Method in Calculus: Formula & Examples

from Calculus: Help and Review

Chapter 3 / Lesson 7
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