hw37 - 1 2/14/11 HW 37 : Divergence Thm (16.9). Rachel...

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12/14/11 HW 37 : Divergence Thm (16.9). 1/4 www.webassign.net/web/Student/Assignment-Responses/last?dep=3285601 Current Score : 20 / 20 Due : Tuesday, December 6 2011 11:00 PM EST 1. 4/4 points | Previous Answers SCalcET6 16.9.AE.02. Video Example Tutorial Online Textbook EXAMPLE 2 Evaluate ∫∫ F · d S , where F ( x , y , z ) = xy i + ( y 2 + e xz ) j + sin ( xy ) k and S is the surface of the region E bounded by the parabolic cylinder z = 1 - x 2 and the planes z = 0, y = 0, and y + z = 3 . (See the figure.) SOLUTION It would be extremely difficult to evaluate the given surface integral directly. (We would have to evaluate four surface integrals corresponding to the four pieces of S .) Furthermore, the divergence of F is much less complicated than F itself: div F = x ( ) + y ( y 2 + e xz ) + z ( sin ( xy )) = Therefore, we use the Divergence Theorem to transform HW 37 : Divergence Thm (16.9). (Homework) Rachel Pereira MA 261 Fall 2011, section 031, Fall 2011
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This note was uploaded on 12/14/2011 for the course MATH 261 taught by Professor Gabrielov during the Fall '10 term at Purdue University-West Lafayette.

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hw37 - 1 2/14/11 HW 37 : Divergence Thm (16.9). Rachel...

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