Can Vector Field G on R^3 Exist?

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Homework Statement


can there be a vector field G on R^3 such that G=<xsiny, cosy, z-xy>?


Homework Equations





The Attempt at a Solution

\
the answer is no, but i don't understand why. any help is appreciated, thanks
 
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G IS a vector field on R^3. I don't think you have the question right.
 
i checked again, i have the question right, and in the back of the book it says no
 
Ok. Then what is your definition of 'vector field'?
 

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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