00:01
Okay, just for simplicity, i put the graph this way, which is x is going up, so this is, the radius is 2, right? and then we also have the n vector, which is, i mean, not the n vector, the way the surface integral works, right? like, something like this is dx, the formula is dx, like d1 plus dx dy squared plus dx dz squared, right? remember this? and then of course, da there.
00:54
Okay, so then let's figure that out, okay? so that is gonna be, f is z squared, and that part is 1 plus dx dy is 2y squared plus 2z squared, and da, and da is actually this.
01:17
So, and we're gonna use that as theta, 0 to 2 pi, and y is gonna go from 0 to, or r is gonna go from 0 to 2, and then z is r sine theta, y is r cosine theta because of the circle, right? so then we're gonna do r squared sine squared theta in parentheses, 1 plus 4y squared plus z squared is 4r squared, and then we're gonna do r dr d theta over here, okay? so let's do the r part first.
02:11
R cubed, so we're gonna have r cubed sine squared theta times 1 plus 4r squared dr d theta, 0 to 2 pi, and 0 to 2, and let's see what we can do here...