- #1
ChemEng1
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Homework Statement
Show that: [itex]\left(\int^{0}_{1}\frac{x^{\frac{1}{2}}dx}{(1-x)^{\frac{1}{3}}}\right)^{3}\leq\frac{8}{5}[/itex]
Homework Equations
Holder inequality.
The Attempt at a Solution
First, I took the cube root of each side. This let me just deal with the 1-norm on the left. Then I broke the function into 2 parts: f=numerator. g=1/denominator. The 2-norm of each function is integrable. |f|2=(1/2)^(1/2). |g|2=3^(1/2). |f|2*|g|2=(3/2)^(1/2)>(8/5)^(1/3), which is counter the claim. So I obviously missed something.
Where is the flaw in this approach? Are there better approaches to this problem?