I am really struggling with this one:(adsbygoogle = window.adsbygoogle || []).push({});

Calculate [tex] \Int F.ndS [/tex], where

[tex] F = a * x^3 * i + b*y^3*j + c*z^3*k [/tex]

where a,b and c are constants,

over the surface of a sphere of radius a, centred at the origin.

note that F and n are vectors (sorry, tried to type them in bold...but it doesn't work)

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So, this is my attempt:

convert everything in polar coordinates and integrate it

where

dS = r^2*sinx*cosz (

for only a hemisphere though...I would multiply it by 2 afterwards to make it a sphere)

the final integral is then:

[tex] dS = \Int {a*dS} = \Int {r^3 (a*sin^3x*sin^3z + b*sin^3x*sin^3z + c*cos^3x) * r^2*sinx*cosz} [/tex]

And this is just a mess. What is wrong here?

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# Homework Help: Surface integral

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