Solving Parseval's Identity: Is This Correct?

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Homework Statement


Is this correct (in the document)?



The Attempt at a Solution


I have a feeling it is not.
 

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The attachment has the be approved, and that might take a while. Can you type up the Identity?
 
The first line
\int \left|\phi(x)\right|^2 dx= \int \left|\psi(p)\right|^2 dp[/itex]<br /> is correct (and is the statement of Parseval&#039;s identity). The second line<br /> \int \left|\phi(x+1)\right|^2 dx= \int \left|\psi(p+1)\right|^2 dp[/itex]&lt;br /&gt; does NOT follow from the first.
 
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Halls could you approve it instead of just taking a peek for yourself :P?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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