Finding Potential Function for Vector Field F

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Homework Statement



Consider the vector field F= 2xi - 4yj + (2z - 3)k.

Find the potential function for F.

Homework Equations





The Attempt at a Solution

 
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what is the definition of potential function?? or in a more matematicl sense what is an exact differential?

use the knowledge you have on integral and derivatives ;)

Marco
 
I think it's just the integral of the vector field..
 
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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