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Home » College Playground » Calculus - Real Analysis » Solved Problems
 
Definite Integral and Inequality
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kunny
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer


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#1
Definite Integral and Inequality
1989 Himeji Institute of Technology
Prove the following inequality.

\int^\pi_0 \sqrt{x(\pi-x)}\sin x\sin (\pi-x)dx<\frac{\pi^2}{4}

PostPosted: Fri Jan 28, 2005 9:12 pm  Back to top 
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Diogene
Yang-Mills Theory
Yang-Mills Theory

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#2
Remember for continuous function (Cauchy) : \frac{f}{g}\neq constant \Longrightarrow \int fg < \sqrt{\int f^2}\sqrt{\int g^2}
f = \sqrt{x(\pi - x)} , g = sin(x)sin(\pi -x) = sin^2(x) , .. and son on ..
Cool

PostPosted: Sun Jan 30, 2005 2:10 pm  Back to top 
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kunny
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer


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#3
That's right! Smile

PostPosted: Mon Jan 31, 2005 4:44 pm  Back to top 
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