1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integral inequality
  1. An integral inequality (Replies: 2)

  2. Integral inequality (Replies: 1)

  3. Integral inequality (Replies: 1)

  4. Integral Inequality (Replies: 6)