0:00
Hello.
00:01
So, given our lorentz curve by the equation, y is equal to x square times e to x minus x minus 1, the genie index is going to be equal to 2 times the integral from 0 to 1 of x minus f of x d x .x.
00:15
So that's 2 times the integral from 0 to 1 of x minus x squared times e to the x minus 1 d x.
00:23
So we just first consider the integral here of x minus x squared times e to the x minus 1.
00:29
We can use integration by parts here where we let you be equal to x squared.
00:37
And then we have that dv is going to be equal to e to the x minus 1 dx.
00:44
That gives us that du is just the derivative of x squared.
00:49
So that's 2x dx.
00:51
And then v is just the integral of e to x minus 1, which is going to be e to the x minus 1.
00:58
Okay, then by integration of my parts says that the integral of udv is equal to u times v minus the integral of vdu.
01:08
So we have the integral of x minus x squared times e to the x minus 1 d x is going to be equal to x squared over 2 and then minus a x square times e to the x minus 1.
01:27
And then we get a plus 2 times the integral of x times e to the x minus 1 dx.
01:36
We can then apply integration by parts again on this integral, on this integral here.
01:45
So now we're going to let you be equal to x...