Ziane Final Spr 07

# Ziane Final Spr 07 - Spring 2007 Math 226 FINAL EXAM Prof....

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Spring 2007 Math 226 FINAL EXAM Prof. M. Ziane Please Print: Last name: First Name : Signature: ID# INSTRUCTIONS: 1. NO CALCULATORS ALLOWED AND NO CHEATING PERMITTED. 2. Clearly indicate your ﬁnal answers by circling them. 3. Show all your work. Unsupported answers will not receive credit. 4. In general you do not need to “simplify” your answers, but you will need to evaluate simple numbers. 5. Point values are labeled and there are 100 total points possible. Good luck! May 2nd, 2007 1

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Hints Green’s Theorem Z C Pdx + Qdy = ZZ D ( ∂Q ∂x - ∂P ∂y ) dA Stokes Theorem ZZ S curl F · d S = Z C F · d r The Divergence Theorem: ZZZ E div F dV = ZZ S F · d S 2
Problem 1. (10 points) a) (5 points) Evaluate the integral ZZ D sin( y 3 ) dA Where D is the region bounded by y = x, y = 2 , and x = 0 . b) (5 points) Evaluate using polar coordinates. Sketch the region of integration ﬁrst.

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## Ziane Final Spr 07 - Spring 2007 Math 226 FINAL EXAM Prof....

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