Switch the divergence coordinate system

oronanschel
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Homework Statement


i have the divergence in the (x,y,z) Cartesian as \frac{dA_x}{dx}+\frac{dA_y}{dy}+\frac{dA_z}{dz}

and the assignment is to transfer it to cylindrical system (r,{\phi},z), by any way i choose.



Homework Equations




tried with the chain rule, but i am doing something wrong, though
i get the gradient in the cylindrical system
 
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It is impossible to tell you what, if anything, you are doing wrong if we cannot see what you did!
 
look at 1 then 2

then there is 1+2

in the left side there are some derivatives , and variables
transformation to explain


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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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