00:01
Okay, let's look at this region.
00:01
We know when x is zero, y is going to be five over two, right? cosine of zero is one.
00:07
So it's going to come like this because the cosine curve goes like that.
00:11
So really, we have this region, and we know center of mass is on the y axis, so x bar is zero, and y bar is y rho density da over mass, which is that.
00:32
So let's calculate the mass first, which is zero to pi over eight times two, and then zero to five over two cosine of x dy dx, right? which is five over two cosine x dx from zero to pi over eight, all times two, then that cancels out.
01:04
So this one gives me 1 .9134.
01:11
And then the other integral, zero to pi over eight times two, of course, again, zero to five over two cosine of x y dy dx.
01:27
So this is going to be y squared over two from zero to five over two cosine x, which is, also there's two out there, so let's get rid of that, these two...