00:01
Find the volume of the solve that lies between x squared plus y squared equals 1, so that's r squared equals 1, and x squared plus y squared plus z squared equals 4.
00:12
So that's the same thing as z squared equals 4 minus r squared.
00:18
So the bounds that we get from this is 0 less than equal to r less than equal to 1.
00:25
That's from this guy.
00:26
And then here we get 0 less than equal to less than equal to less equal to z less than equal to the square root of 4 minus r squared and then theta theta just has to be between 0 and 2 pi so we get the integral from 0 to 2 pi the integral from 0 to 1 the integral from 0 to 1 the integral from 0 to the square root of 4 minus r squared times r d z d r d tether so this is 0 to 2 pi, 0 to 1.
01:20
And then remember over here, we were just integrating with respect to z, not with respect to r.
01:26
So we just end up with r times z evaluated from 0 all the way up to this guy.
01:36
So we end up with r times the square root of 4 minus r squared.
01:42
Dr, d theta.
01:46
Now we can do u equal to 4 minus 2...