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Using Stokes theorem I seem to find the integral value as $2\pi r^2$. Can anyone help me if I am right? How do i do it without using Stokes theorem?

$$C=\oint\limits_K \mathrm d \mathbf r\cdot \mathbf A$$

Where $\displaystyle \mathbf A=\frac{1}{2}\mathbf n\times\mathbf r,\quad \mathbf n\cdot\mathbf n=1$, and $K$ is a circle with radius $R $ and $\mathbf n$ is the normal to the plane where the circle lives.

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