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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, February 07, 2006

### Scribe

Today in class we worked on a few antiderivatives. We learned the Simpson Sum which is the best way to find the integral with an estimate.
Simpson Sum = (Tn* + 2Mn*)/3
*(n is a subscript)

The Definite Integral from 0 to 4 for x² dx.
the antiderivative of xÂ² is x^3/3
Evaluate for when x =4 ansubtractct when x=0.
= 1/3(4)^3 - (1/3)(0)^3
= 64/3
= 21.3333

Using Simpson Sum, you get 21.3333, when n = 2.
The Simpson Sum is a combination of the Trapezoid Sum and twice the Midpoint Sum, then divide by 3.
The Trapezoid Sum is a combination of Left Hand Sum and Right Hand Sum, divided by 2.
The Midpoint Sum can be found by using your calculator and one of the programs on the calculator.
The next scribe is Chris.