00:01
Let's start by drawing these graphs.
00:05
So, y equals x squared.
00:08
It's going to look like this.
00:35
And x equals 2y minus y squared is going to look like this.
00:43
And i should have drawn this bigger, but this is the area trying to find.
00:49
They cross at the origin.
00:52
In this point here is one, and you can solve that by a logistic.
00:57
So we substitute x into here.
01:00
Y squared equals 2y minus y squared this becomes 2y squared is 2y these cancel so we're left with 2y 2 so y equals 1 so this curve here is going to be a lower boundary because it's underneath in this portion and this curve here is the other boundary because it's on top of the issue area so dx d y oops d y so this is our, this is this curve, so we have 2y minus y squared, y squared from 0 to 1.
01:49
This is integral from 0 to 1 of y squared minus 2y minus y squared, dy.
02:01
So this becomes 0 to 1 of y squared minus 2y plus y squared, d y, so this becomes 0 to 1 of y squared minus 2y plus y squared, d .y...