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Surface integral

Let $S$ be the surface MATH where $\left( s,t\right) $ varies over some region $D$. The surface integral is in some sense a higher dimensional analog of the line integral.

For a real-valued function MATH that is defined on this surface, the surface integral MATH can be evaluated by converting the it into an ordinary integral usingMATHwhereMATHand MATH is the magnitude of the cross product of $\QTR{bf}{q}_{s}$ and $\QTR{bf}{q}_{t}$.

For a continuous vector field MATH defined on $S$, the surface integral of $\QTR{bf}{F}$ over $S$ is given byMATH


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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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