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## Homework Statement

The region bounded by [itex]y=e^-x^2[/itex], y=0, x=0 and x=1 is revolved around the y-axis. Find the volume.

## Homework Equations

[itex]V = \int_{a}^{b} R^2 dy[/itex]

## The Attempt at a Solution

We must first express x in terms of y. So we get

[itex]\ln y = -x^2[/itex]

[itex]x^2 = -\ln y[/itex]

We substitute this to the above volume equation and we get

[itex]V = \int_{0}^{1} -\ln y[/itex]

And without even doing the integration, I know for a fact that this cannot work out since if you integrate a natural log, you get a natural log back and substituting 0 into a natural log gets you an undefined answer.

I think I did something wrong or set up the problem wrong. Any advice would be appreciated!

Oh and if you know latex, could you tell me how to express y=e^(-x^2)?