Integral of cos(8x^2)? multivariable calc

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Integral of cos(8x^2)? multivariable calc

Homework Statement



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Homework Equations



none

The Attempt at a Solution



So i reversed the order...

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and couldn't figure out how to integrate cos(8x^2). I looked at my trig identities, tried on my graphing calc, and even wolfram alpha gave me a strange answer that i can't use.

Either I'm doing something wrong, or missing something obvious.

Thanks
Jake
 
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...dy dx?
 


oh yeah. in my work i should have wrote dydx instead of dxdy good catch. wow. maybe i can solve it now.

lets see...wow... the answer was 0, after a page of work and a few hours of confusion
 
Last edited:
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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