Vector Field Homework: Learn What's Involved

athrun200
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Homework Statement



attachment.php?attachmentid=37437&stc=1&d=1311346565.jpg


Homework Equations





The Attempt at a Solution


What's surprise?
And is my work correct?


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You have a problem: \mathbf{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}.
 
hunt_mat said:
You have a problem: \mathbf{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}.

r is the radius from centre, isn't it?
 
It is.
 

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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