A question on calculus of variations

nenyan
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Homework Statement



δ (∂x'^μ/∂x^β)=0

This equation is on my textbook. I don't quite understand. Where x'^μ is coordinate component.


Homework Equations





The Attempt at a Solution

 
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Is the transformation from x to x' given or what are your symbols supposed to mean?
 
Yes. It's the transformation from x to x'.
δ is Variational symbol.
vanhees71 said:
Is the transformation from x to x' given or what are your symbols supposed to mean?
 
Ok, you must define the meaning of x' or give the complete variational problem. I don't know, what's meant by this symbol!
 

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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