Evaluate the flux of F(x,y,z)=xi + yj + zk

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Homework Statement


Evaluate the flux of F(x,y,z)=xi + yj + zk across the surface q:x^2+y^2+z^2=16, oriented by unit normals.


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The Attempt at a Solution

 
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One: I don't see any attempt at a solution- just integrate!

Two: Since there are no bounds to the surface it looks to me like the flux will be infinite. Weren't there any boundaries given?

Three: You have copied the problem incorrectly. "Oriented by unit normals" makes no sense. There are two unit normals at a point of any surface. The orientation is given by choosing one of them. Oriented by which unit normal?
 

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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