Vector Calculus II: Flux Integrals

Tylerdhamlin
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Homework Statement




F = 2i + 3j through a disk of radius 5 in the plane y = 2 oriented in the direction of increasing y.
Calculate the flux of the vector field through the surface.


Homework Equations





The Attempt at a Solution



I know that I need to calculate the area vector of the surface and then dot that with F, However, I'm in a bit of a brain slump and can't figure out how to calculate the Area Vector.
 
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Well, in the simple case of a planar (flat) area, the area vector is the unit normal multiplied by the usual area element in that plane.
 
Yes. Shortly after the post, I was able to solve this problem. Anyways, thank you for your help.
 
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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