Decoding Art: Understanding the Transformation from Painting to Integral

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dont be scared look at it from mathematical point of view

i just want to understand how they transform the painting to the integral

cant understand what is ds
and why it equals rd(phy)

maybe the confused phu with teta(cause i don't see phi)
i still can't see what that means
?

2ug28nn.jpg
 
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why don't you give the problem description with all related info

if you want the best chance of a reply, you should try and make it as easy as possible for people with fresh eyes to interpret

Also whilst the integrals use multivariable calculus, this is probably better off in the adv. physics forums as it look to be standard electrodynamics
 
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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