Applications to Geometry

Monday, September 20, 2010 - 14:00 - Tuesday, September 21, 2010 - 15:00
WebworkSection8.2.pdf112.27 KB

This section was really an extension of 8.1. Some notes:

  • Remember that the integral's "dx" usually provides one of the dimensions (width, height, length) and so your integrand for area will be a single dimensional function, while your integrand for volume is a 2-dimensional function.
  • We did several examples about cross sections. The only way to get good at these problems is just to practice them. In any case, the last problem on webwork is a bit of a pain. You'll need the area of those triangles. This is easiest to do using the ideas from similar triangles and trigonometry. Specifically, remember that an equilateral triangle has three angles of 60 degrees, and sin(pi/3) is a nice number to work with.
  • We derived the arc length formulas. If you need those, you should derive or memorize those.

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