I have two questions:
I just learned about U-Substitution in class, and while I'm able to apply it, I'm a bit confused on some of the theory behind it.
The thing that most confuses me is that if we take the indefinite integral of f '(x) with respect to "x", that means the term inside the integral is actually the multiplication of f '(x) and dx. I always thought that dx term was just there to show that the derivative was taken w.r.t. "x", I didn't know it was being multiplied by f '(x). Why is this the case?
I'm also just very confused on the integral in general. It seems to me that the integral of something can mean many different things (antiderivative, area under a curve). How are definite and indefinite integrals related and where do they come from?
edit: Please look to my comments on KM101's answer to better understand what I'm asking.
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