00:01
Okay, to convert to polar coordinates, we've got to look at the picture, the area that we're integrating over.
00:09
So first we know x is going from zero to the square root of a squared minus y squared.
00:16
Okay, if you squared both sides out, you'd get x squared plus y squared equals a squared, which we know is a circle.
00:23
But notice it's just the positive part.
00:26
So it's the right -hand side of the circle.
00:28
And then y is going from just zero to y equals a.
00:38
So that cuts off the bottom half.
00:42
Okay, so we're just looking at the top one -fourth of a circle.
00:48
Can remember that x is r cosine theta, y is r sine theta, and dx, d -y, which is d -a, change in area is r -d -theta.
01:05
So don't forget that extra r there.
01:10
Okay, so r is going from zero out to the edge of that circle, which is a circle of radius a, so zero to a.
01:23
And then theta is starting here at theta equals zero, and going here to theta equals pi over two.
01:32
And then y is r -sign theta, and then da is r, dr d -theta.
01:40
Oops, i forgot the dr...