Ok, so this problem appears very simple, so I'm actually surprised that I'm stumped on it, but I'm very suspicious that the answer is in poor algebra skills since I'm thinking I may be forgetting my exponents rule here or applying incorrectly.
Anyway, the problem is to find the volume of a solid of revolution for the function e raised to the -x when and x is equal to or greater than 0, so the definite integral is from 0 to infinite. I have V = pie * the integral from 0 to infinite of e raised to the -x and then squared and I think this is where I'm running into trouble. I'm solving e raised to the -x and then squared as e raised to the and I don't see how you could solve the integral of e raised to the power because you can't do a U sub since du would be 2x and there's no x, so you can't factor out a coefficient...parts doesn't seem applicable, nor does tab, and can't integrate it as is or use algebra to integrate.
So my question is, would e raised to the -x power then squared be e raised to the -2x power instead? Because then that would be simple enough to integrate, then take the limit and solve the problem. I apologize in advance for not having everything in the math notation on here, but for some reason, I can't figure out how to depict e to a power such as -x with the math symbols.