2.2 Determining Volumes by Slicing 

[STARTS AT 12:35]

INSTRUCTOR: Same concept, use the disk method, which says that our area-- or actually our volume. I need to say that differently. Our volume is the integral from a to b of pi f of x squared dx. Now, this is between the function and the x-axis over the interval 0 to 4, and it's around the x-axis. So this does work. 

So this will be the integral from 0 to 4 pi square root of 4 minus x squared dx, which would be 4 pi minus pi x, squaring that and then distributing the pi there, integral from 0 to 4 dx. So we get 4 pi x-- 4 pi is just a constant, after all-- pi x squared over 2. So that would be the 0 is going to be 0. So that just going to be 16 pi minus 8 pi, 8 pi units cubed. 

[ENDS AT 14:07]