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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, March 01, 2006

Scribe for Wednesday

We worked on solving for the volume of a function that is revolved around the y-axis. The integral for the interval [a,b], the inner function is the length times the width times the height.

V= (2(3.141...)x)(f(x))

The height is represented by f(x), the width is dx, the length is 2(pi)x.
In class, one of the examples was f(x)=√(-x+3)

V=2(pi) √(-x^3 +3x²)

When the graph is revolved around the line x=5

V=2(pi) (5-x)√(-x+3)

The second part of class was about the average value of a function. Which can be defined as:

[f(x1)+f(x2)+f(x3)+...+f(xn)]/n

dx= (b-a)/n
n=(b-a)/dx

1/(b-a) f(x)
The Average Value of a Function is defined by the previous expression. This expression can be used to find the mean value or f(c).
The next scribe is Chris



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