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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.

Wednesday, January 11, 2006

Integral or Derivative?

Todays class(and yesterdays class for the three of us not writing our english) started with Mr. K asking us to solve a lot of integrals, but geometrically, not using the fundamental theorem. The integrals were all on the function f(t)=t with the interval between 0 and a series of different values of b. That was all fine until we came upon integrals with a negative value for b. However Mr. K explained that we solve them exactly how we solve any other integral.
For example: on the interval 0 to 1, the integral is solved F(1) - F(0)
on the interval 0 to -1, the integral is solved F(-1) - F(0)

After that, Mr. K asked us to complete a table of values with values ranging from -4 to 4 for the function

We were then asked to graph it, the graph itself turned out to be the same as the function f(x)=(1/2)x². The function f(x)=(1/2)x² is also the anti-derivative of the identity function(f(x)=x). The lesson is a demonstration that integration and derivation are inverses of each other, just in the way that addition and subtraction are.
The function A(x) is an example of an accumulation function. It is called an accumulation function because as x progresses, the function accumulates area.

The next scribe will be..... Jayson

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