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Find the volume of the solid formed by rotating the region enclosed by y = e^(1x + 2), y = 0, x =...

Question:

Find the volume of the solid formed by rotating the region enclosed by {eq}\; y = e^{1x + 2}, \; y = 0, \; x = 0, \; x = 0.8 \; {/eq} about the {eq}x {/eq}-axis.

Volume of solid:

Volume of solid defined by the curve y=f(x) and rotated about a given axis is given by

{eq}V=\int_{a}^{b}A(x)dx{/eq}

where A(x) is the area of the solid.It is defined as

{eq}A(x)=\pi \text{(radius)}^2{/eq}

When the solid is between two curves f(x) and g(x) then area is given by

{eq}A(x)=\pi (\text{(outer radius)}^2-\text{(inner radius)}^2){/eq}

Answer and Explanation:

x ranges from 0 to 0.8

and the curves that define the solid are {eq}y=e^(x+2){/eq} and y=0

{eq}\begin{align*} A&=\pi(e^{(x+2)})^2\\ &=\pi...

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How to Find Volumes of Revolution With Integration

from Math 104: Calculus

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