Find the volume of the solid generated by revolving the region in the first quadrant bounded by ...

Question:

Find the volume of the solid generated by revolving the region in the first quadrant bounded by {eq}y = e^x {/eq} and x-axis, from {eq}x = 0 \enspace to \enspace x = \ln 5 {/eq} about the y-axis.

Using the Shell Method to Calculate the Volume of a Solid of Revolution:

Suppose we have a function {eq}y = f(x) {/eq} defined on an interval {eq}0 \leq x \leq b {/eq} and we revolve the graph of {eq}f {/eq} around the {eq}y {/eq} axis. We can use the Shell Method to calculate the volume of the resulting solid, using the formula

{eq}V = \displaystyle 2\pi \int_0^b x f(x) \: dx. {/eq}

Answer and Explanation:

We are given the function {eq}y = e^x {/eq} bounded below by the {eq}x {/eq} axis and on the left and right from {eq}x = 0 \enspace to \enspace x =...

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How to Find Volumes of Revolution With Integration

from Math 104: Calculus

Chapter 12 / Lesson 5
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