I'm attempting to find the volume of the solid obtained by rotating the region under the curve:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]e^{-x^2}[/tex] Bounded by y = 0, x = 0, and x = 1.

I've done quite a few of these problems before, however, none of them have involved an exponential. If I recall correctly [tex]e^{x^2}[/tex] cannot be integrated, at least symbolically. So, therein lies the problem.

So far this is what I've done:

[tex]\int_0^1 \pi\left( e^{-x^2}\right)^2 dx[/tex]

[tex]\pi\int_0^1 e^{-2x^2} dx[/tex]

I've integrated that integral with Mathematica, and it returns a function that uses the error function, which I doubt is anything that I'm expected to come up with in this class.

Therefore, the only way I believe this problem can be completed is by finding the area under [tex]e^{2x^2}[/tex] on the interval [tex]\left[0 ,1\right][/tex] using a Riemann Sum.

Any thoughts?

Edit: Fixed a typo involving a constant in the integral.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Finding volumes of solids involving exponentials

Loading...

Similar Threads for Finding volumes solids |
---|

I N-th dimensional Riemann integral |

I Can i find this integral in a simpler way |

I Q about finding area with double/volume with triple integral |

I Finding a unit normal to a surface |

I Finding value of parameters to fit some data |

**Physics Forums | Science Articles, Homework Help, Discussion**