00:01
Alright, we're given two functions and we want to find the area between them, so i graphed them on a graphing calculator online, and this is what i got.
00:11
The red one is the first one, which makes sense because of the x squared, it's always positive, and then the blue one is the second one, and you can see it's below the x axis on the negative side of the y axis and above, because x is negative over there and x is positive over on the right hand side.
00:39
Okay, so you can see that the area you want is right in here, so we need to find these two points of intersection, you can see that they are zero and one, but let's prove that.
00:52
X squared e to the minus x equals x e to the minus x.
00:58
E to the minus x can never be zero, so we can divide it out, so we get x squared equals x squared minus x equals zero, x times x minus one equals zero, so x is zero and x is one, so that's what we're going to integrate from...