Find g'(x) by using Part 2 of the Fundamental Theorem of Calculus.

Here is what I have done so far:

Assuming that these two steps are correct (are they?), how do handle the fact that is undefined?

Thanks!

Printable View

- Mar 31st 2011, 08:13 PMjoatmonFTC2 - Not sure how to deal with this one
Find g'(x) by using Part 2 of the Fundamental Theorem of Calculus.

Here is what I have done so far:

Assuming that these two steps are correct (are they?), how do handle the fact that is undefined?

Thanks! - Mar 31st 2011, 08:23 PMpickslides
Those steps aren't quite right, consider

- Mar 31st 2011, 08:28 PMTheChaz
Obviously, you are able to compute the integral and

*then*take the derivative. This will not always be the case, and eventually (!) you will become familiar with the following:

Oh... it's on wikipedia!

Fundamental theorem of calculus - Wikipedia, the free encyclopedia

Just replace the "t" inside the integral with x.

If your upper limit has an "interesting" derivative, you'll need to use the chain rule. - Mar 31st 2011, 09:18 PMjoatmon
I took the derivative instead of the antiderivative. Duh. Thanks, pickslides, for pointing that out. Chaz, the question specifically requires that I use part 2 of the FTC. Your post uses part 1 (at least that's what our book calls them). The question actually makes us do it both ways. I got the answer easily using part 1, but when I did it with part 2, I got hung up. Now I know why.

Thanks to both of you.