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Integral inequality

  • Thread starter phyguy321
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  • #1
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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
 

Answers and Replies

  • #2
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[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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