The Fundemental Theorum Of Calculus

[undrcvrbro]

the fundamental theorem of calculus

Homework Statement

\int^{3}_{2}12 * (x^2-4)^(5) * x

Homework Equations

U substitution.

The Attempt at a Solution

This is part of a FTC problem, but I find myself stumbling a little bit with the u substitution still. I'm not sure when the du= the derivative of the u, and when it is just the numbers left over.

Like in this situation, I set u=x^2-4. Would du=2x or 12x?

 

[Tedjn]

If u = x² - 4, then the derivative du/dx = 2x. Although we technically shouldn't break up the derivative, it turns out we can do it without affecting results, and all our steps are justifiable with the chain rule. Commonly, however, we treat du/dx as a fraction, and find du = 2xdx \implies dx = du/(2x).

 

[undrcvrbro]

Thanks. Now that I look closer, I think my only issue was that I seemed to have been seeing some coincidental pattern on a few of my problems a while back and drew the conclusion that it was mathematically correct. I always do dumb stuff like that