Vector field equation - Find work of the field

asi123
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Homework Statement



I have this vector field equation, the first part of the question is to find the potential equation for it, I found it.
The second part of the question is to find the work of the field through this path.
My idea is to plug t in the r equation, because I'm not sure but I think (x,y,z)=(component of r), is that right? and that way I find the start point of the path and the end point, plug it into the potential equation and that's it, is that right?

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The Attempt at a Solution

 

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Sure, that's it.
 


Dick said:
Sure, that's it.

10x, it seemed so easy, and they gave 10 points for it (it's a question from a test), so I got confuse...
 


Well done! I didn't have to help much, did I? I like that.
 
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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