Module 1 : A Crash Course in Vectors
Lecture 5 : Curl of a Vector - Stoke's Theorem
  The area element on the surface of the northern hemisphere is .
   
  Hence the surface integral is
 
\begin{eqnarray*} \int_0^{2\pi}d\phi\int_0^{\pi/2}\frac{f(r)\cos\theta}{R\sin\th... ...&=& 2\pi Rf(R) \int_0^{\pi/2}\cos\theta d\theta\\ &=&2\pi Rf(R) \end{eqnarray*}

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