Explanation of this slideshow (1)

Explanation of this slideshow (1) • • Last semester I taught MA233 and wanted illustrations for double integrations of volume. I wasn’t happy with the two in the textbook: Explanation of this slideshow (2) • • • • • I created several illustrations to replace those two. I put them in a PowerPoint presentation, which begins on the next slide. Just this semester I added these two explanation slides, for you MA307 readers. The next slide contains no 3D illustrations. (I left it there for historical purposes.) All the others do. View this as a slideshow, because there are transitions and animations that will not occur otherwise. In Calculus II, we computed area under curves as integrals An integral is a limit as you add rectangles indefinitely.  b a  n b  a    b  a  f x dx  lim    n f a  k  n  n     k1  We can apply the same technique in three dimensions Goal: find the volume under this surface. More rectangles, better approximation Many more rectangles, much better approximation The integral will again be a limit, as if infinitely many rectangles