Solve Integral Inequality with cos(x): \int\sqrt{xcos(x)} dx 0..Pi/2

[phyguy321]

Show that $$\int$$$$\sqrt{xcos(x)}$$ dx from 0..Pi/2 $$\leq$$ Pi/2 $$\sqrt{2}$$


Having problems with the cos(x) part. Maple gives -sqrt(2)*EllipticK((1/2)*sqrt(2))+2*sqrt(2)*EllipticE((1/2)*sqrt(2)) for the integral of the cos part.

what are EllipticK and EllipticE and how are they evaluated?
so lost right now

 

[sutupidmath]

$$cosx\leq 1=>xcosx<x=>\sqrt{xcosx}\leq \sqrt{x}$$ now

$$\int_0^{\frac{\pi}{2}}\sqrt{xcosx}\leq \int_0^{\frac{\pi}{2}}\sqrt{x}=\frac{1}{2}\frac{2}{3}x^{\frac{3}{2}}|_0^{\frac{\pi}{2}}=\frac{1}{3}\frac{\pi}{2\sqrt{2}}<\frac{\pi}{2\sqrt{2}}$$