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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.

## Saturday, January 14, 2006

### Composite Functions and Integrals

Friday, we learned about accumulation functions that are a composite of functions. when finding the derivative of a composite of functions involving integrals, is not as difficult as it may seem.

a= 3
b= x^2
f(x)= √(t^6 +1)
dy/dx = (√((xÂ²)^6 +1)(2x)
The inner function is xÂ² and the outer function is the square root function.
dy/dx = 2x√(x^12 + 1)

Another part of the class was about the area between the curve and the x axis. Integral means signed area, and Area is not the Integral. Due to the fact that many graphs have roots and an area below the x axis as well as above it, to compensatete for this, you have to take the absolute value of the function.
abs(f(x))
If you have two functions, the area between them involvesolvingng for the intersection points, then finding the integral of the function that is higher and then subtract the integral of the lower function.
The next scribe is Sarah.