Meden Agan's latest activity
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.How about differentiation under integral sign or integral representation of ##\arcsin##? What do you think?
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Mhm... A delightful surprise! Most likely my instructor took that integral from there. However, I would be interested to hear what we...
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MMeden Agan reacted to renormalize's post in the thread Prove that the integral is equal to ##\pi^2/8## with
Like.
It turns out that this very integral was posted 5 days ago on Mathematics Stack Exchange by "Dan" (is that you @Meden Agan ?)... -
MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
That's why I haven't tried it so far. ##\sqrt{f(\alpha)f(-\alpha)}## looked like a perfect circle, but this wasn't the case...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Mhm... Do you think that identity can make anything easier? IMO, probably complicates the integrand even more.
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
I gave WA the integrand, and here is what you want to calculate: the area below ... I also fed WA with the integral...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.No. My instructor proposed that integral.
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.No, but I just felt it was the easiest way to evaluate it.
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
I think I made a step forward. Say we abbreviate the integral by $$...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.I have no idea how to handle that...
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
How did you show equivalence without rescaling ##x## which would be necessary to change the upper bound of the outer integral? A...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Mhm, good point. But what I'm trying to say is something different. I am saying I discovered that the two double integrals...
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
My result is complicated, too. I wrote ##\theta=\alpha## since it is easier to type with my keyboard settings. I got for the entire...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.I get nothing. We have $$I = \int_0^{\sqrt{2}/4}...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.I mean in the double integral, if we set ##t= \sqrt{\dfrac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}}##, bounds of the outer integral...