Hi everyone, I would like help with the following question please:

A horn is generated by rotating the curve y = 1 + e^-x about the x-axis between x = 1 and x = 3. Find its volume to three decimal places.

I figured that the volume can be attained by finding the integral of (1+e^-x)^2 from x=1 and x=3 and then multiplying it by pi, however, I do not understand why we do not subtract the volume of the cylinder formed by the asymptote? How exactly does integration work here to find the volume, thanks!

Thank you sooo much !!!

A horn is generated by rotating the curve y = 1 + e^-x about the x-axis between x = 1 and x = 3. Find its volume to three decimal places.

I figured that the volume can be attained by finding the integral of (1+e^-x)^2 from x=1 and x=3 and then multiplying it by pi, however, I do not understand why we do not subtract the volume of the cylinder formed by the asymptote? How exactly does integration work here to find the volume, thanks!

Thank you sooo much !!!

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