Jan 24 - Area between curves

Today should feel pretty comfortable considering that it's been 7 weeks (less one day) since we've met as a class. (!) It's an application of integration and we've actually calculated areas using integrals already. There will be two new things that you will see. First we'll use two functions as boundaries, rather than having the x-axis always be one of the boundaries, thus the integrals will usually be some Integral((f(x) - g(x)) dx rather than just Integral(f(x) dx). The second new thing will be more complicated and that is that we will occasionally set up integrals with respect to y (instead of x). It shouldn't be more difficult but it always seems to be - it's just kind of bizarre to do things "up/down" rather than "left/right." Fortunately we won't do much of the dy thing.

If you can get yourself believing why the integral works and conceptually understanding what we're doing, then the next week or so will follow well.

Notes from today are attached.

p1

p2