CALCULUS Understanding Its Concepts and Methods

Surface integral

Let be the surface where varies over some region . The surface integral is in some sense a higher dimensional analog of the line integral.

For a real-valued function that is defined on this surface, the surface integral can be evaluated by converting the it into an ordinary integral usingwhereand is the magnitude of the cross product of and .

For a continuous vector field defined on , the surface integral of over is given by

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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.