00:01
Okay, so here we are going to find all those polynomials, g, such that h of t multiplied by g of t, is going to give us integral from 01 equals 0.
00:18
That is, let me be more precise.
00:20
Let's write g of t equals a, t squared, plus b, t plus c, let's find a, b, t, and.
00:30
C such that h g which is equal to an integral from 0 1 of a t squared plus b t plus c multiplied by 2t plus 1 in the t equals 0 okay so how are we going to do it well this is actually pretty easy we are going to have what we are going to have that this guy is an integral from 0 to 1 of 2a t cubed plus 2 bt squared plus 2 bt squared plus 2 c t then plus a t squared plus bt plus c in the t so we want this guy to be equal to 0 okay so let's let's rewrite this algebraic expression in a different way.
01:47
Here we can write, okay, 2a t cubed, plus what, plus a plus 2b, t squared, plus 2c, okay, 2c plus b, and finally plus c in the t.
02:25
Okay now let's compute the integral of this guy what is this thing okay here we're gonna be like very fast so here we are gonna have 2a over 4 plus a plus 2b over 3 plus 2c plus b over 2 c and we want this thing equals 0 to be equal to 0 so now let's reorder it a little bit here we are going to have hey a over 2 plus a over 3 plus okay to b over 3 plus b over 3 plus b over 3 plus b over 2 plus and we want this thing to be equal to 0.
03:41
But now this guy is what? this guy is 6 here.
03:46
So 3 plus 2, 5a over 6.
03:50
This guy here is, okay, 6 year.
03:56
So for b plus 3, so 7b over 6.
04:01
So 7b over 6 and this one is just 2c...