Okay to integrate this function. What I noticed first is that I have a fated to the three halves. And if they did to the one half, and I know that the derivative of data to the three halves hesitated to the one half in it. So that tells me I need to make you be the stated to the three halves. And then the square root of that is gonna be part of D U. So let u equal data to the three halves, then do you? Is three house data to the one half d theta. So we have the data to the one half right here. I don't have a three have. So I'll just put one. Went out in front here, backwards, the inverse. All right, Uh, if they d equals zero than you equals zero to the three house, which is zero, if they do equals the cube root of pi squared. That's pi to the two thirds than you equals pi to the two thirds to the three halves, which is just pie. All right, so I'm integrating two thirds zero pie. Cosine squared you and then this and this That's do you okay? do integrate the coastline square to have to put in an identity. So let's do that. Now. The identity is one plus the casino of to you over to do you. So this too and this to cancel out. So now I have one third the integral jeered a pie one plus the cosine of to you, Do you? It's a one third zero pie one, do you? Plus one third zero pie co signed to you. Do you can. I did that separately so that you can see what happens with this too. Right here. But here we get one third you from zero pie. Plus, here we get one third. I'm gonna have to make another substitution. I'm gonna let w b to you. And so d. W is to do you. So I needed to in there, which will put a one half out here. Okay. If U equals zero, then w equals zero. If you equals pi, then w equals two pi. So we have 0 to 2 pi co signed w d w. All right, so here we get one third pie. Here we get plus 1/6. The inner girl. The cosine is the sign up w from 0 to 2 pi and when you plug both those in, you get zero. So one third pie should be the answer to this one or pi over three.