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Integral inequality

  1. Oct 6, 2008 #1
    Show that [tex]\int[/tex][tex]\sqrt{xcos(x)}[/tex] dx from 0..Pi/2 [tex]\leq[/tex] Pi/2 [tex]\sqrt{2}[/tex]


    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
     
  2. jcsd
  3. Oct 6, 2008 #2
    [tex] cosx\leq 1=>xcosx<x=>\sqrt{xcosx}\leq \sqrt{x}[/tex] now

    [tex] \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}}[/tex]
     
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