00:01
So for this integral, we're going to be using integration by parts, and we're going to let u here equal x, and then we're going to let dv equal sign of x divided by 2.
00:14
And if you don't know integration by parts, you basically pick a u variable and a dv variable, and then you solve for du, which is just the derivative of your u variable.
00:23
In this case it would be 1 or just i'll even just put dx and then we solve for our v variable here so we're integrating or anti -differentiating and the integral of sine of x divided by 2 that's going to be 2 times it's actually going to be negative 2 times cosine of x divided by 2 and we can see if we took the derivative of this function here we would have negative sign times 1 1⁄2 which would just give us a of x divided by 2.
00:54
And so now that we have these four variables, i'm just going to go ahead and move them up here.
01:01
And we're going to set this equal to u times v minus the integral of v, du.
01:08
So here, u is equal to x, v is equal to negative 2, cosine of x divided by 2, and then we have minus the integral of v, which is negative 2, cosine of x divided by 2.
01:23
2 times du, which is just equal to dx...