- #1

greg_rack

Gold Member

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- Homework Statement
- Calculate the volume of the solid generated by rotating around the y-axis the plane region delimited by curves:

##y=e^x##

##x=0##

##x=1##

##y=0##

- Relevant Equations
- Definite integrals definition

First, I calculated the inverse of ##y=e^x## since we're talking about y-axis rotations, which is of course ##x=lny##.

Then, helping myself out with a drawing, I concluded that the total volume of the solid must've been:

$$V=\pi\int_{0}^{1}1^2 \ dy \ +(\pi\int_{1}^{e}1^2 \ dy \ - \pi \int_{1}^{e}ln^2y \ dy)$$

However this leads me to a wrong result; I must be getting something wrong, probably in the second integration(from 1 to e)...

Then, helping myself out with a drawing, I concluded that the total volume of the solid must've been:

$$V=\pi\int_{0}^{1}1^2 \ dy \ +(\pi\int_{1}^{e}1^2 \ dy \ - \pi \int_{1}^{e}ln^2y \ dy)$$

However this leads me to a wrong result; I must be getting something wrong, probably in the second integration(from 1 to e)...