CAA: Christian Anime Alliance

My instructor unfortunately assigned us homework with almost no in-class explanation of how to do this.

I'm stuck on number 2. This is probably really easy, which is why I feel so stupid now. Here's the problem:

"Verify directly that F is an antiderivative of f."

The problem is:

F(x) = x e^x + (pi); f(x) = e^x (1+x)

I really, really just don't have any clue where to even begin with this one...I know the antiderivative of e^x is still e^x, but other than that, I'm lost.

You have two options. The first (and easiest), is to realize that if F is the a.d of f, then f must be the derivative of F. In that case, you simply need to differentiate F and verify that it is equal to f (which it is). The second approach is to work out the integral of f, in which case, I believe you will have to use integration by parts. I'm guessing though that the former approach is the one you will find in the solutions manual.

Thanks...you're right. I just took the derivative of F(x), which was easy enough, and showed it that way...no wonder I didn't understand how to do it the other way. Integration by parts isn't for another 10 chapters. ><