Hi PF!(adsbygoogle = window.adsbygoogle || []).push({});

So let's say I have some vector field, call it ##\vec{F}## and let ##\vec{F}## be 2-Dimensional and suppose I wanted to compute ##\iint_D \nabla \cdot \vec{F} dD##. Using green's theorem we could write ##\iint_D \nabla \cdot \vec{F} dD = - \int_{\partial D} \vec{F} \cdot \hat n dS## where ##\hat n## is the outward oriented surface normal. Now if ##D = [0,1] \times [0,1]## I may use the formula to find the solution. Can you tell me what I'm doing wrong? $$\int_{\partial D} \vec{F} \cdot \hat n dS = \int_0^1 \vec{F} \cdot (- \hat j)dx + \int_0^1 \vec{F} \cdot ( \hat i)dy+\int_1^0 \vec{F} \cdot (\hat j)dx+\int_1^0 \vec{F} \cdot (\hat i)dx$$

I know there is another way to write Green's Theorem but how to do it this way?

Thanks a ton!

Josh

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# Green's Theorem Applied

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