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# AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

## Tuesday, January 17, 2006

### Blogging on Blogging on Integrals

When it comes down to integrals, they are kind of confusing. The fact that integrals and derivatives are inverses confuses me. I think the the hardest part of this unit was composite functions involving integrals. Finding the derivative of an accumulation function requires the chain rule.

a=0
b=2x
f(x)= f(t)= tÂ²

You take f(t)substitutee 2x for t and derive and multiply that by the derivative of 2x.

F' (x)= (2x)(2)
F'(x)= 4x

I think that the confusing part of it is remembering that the upper limit or 2x in the previous example, is the inner function and that the outer function is f(t). Having clarity on this makes such a difference when solving for the derivative of F(x).