Solve Integral of cos(y^2) - Calculus

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Can anyone help me with the integral of cos(y^2)?
 
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Possibly. Can you reduce cos(y^2) down and express it in terms of sin(y) and cos(y)?
 
not really. I'm finding functions, given the gradient...

((e^x)*cos(y^2))i - (2y(e^x)sin(y^2))j
 
I reckon you can. How about if you write cos(2y)=cos(y+y)=...
 
cristo - its cos (y^2), not 2y :(

caaron3 - it has no elementary solution, though if you really want some sort of a solution, the anti derivative is in terms of the Cosine Fresnel Integral, so look that up.
 

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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