Wednesday, April 5, 2017

lecture 28: triple integrals

I'll be working examples from section 13.4. You should be aware of this interesting pattern:
  1. $\int_I 1 \, dx = length(I)$ where $I$ is an interval on the $x$-axis.
  2. $\iint_D 1 \, dA = area(D)$ where $D$ is a region in $\mathbb{R}^2$.
  3. $\iiint_E 1 \, dV = volume(E)$ where $E$ is a solid region in $\mathbb{R}^3$.
If there is time we may look at the cylindrical coordinate system (13.5).