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Unformatted text preview: φ = φ but inside the sphere ρ = ρ , assuming that density is constant. 6. (15 pts.) Let R be the region in the x , y plane bounded by xy = 1, xy = 2, xy 2 = 1 and xy 2 = 3. Write Z Z R x dA as an iterated integral in the variables u and v , where u = xy and v = xy 2 . 7. (15 pts.) Use Green’s theorem to evaluate I C ( x 3y 3 ) dx +( x 3 + y 3 ) dy , where C is the pictured curve, consisting of two circular arcs and two line segments. 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Figure for problem 7. 8. (5 pts.) If ~ F is the vector ﬁeld shown, can ~ F be conservative? Why or why not? –1 –0.8 –0.6 –0.4 –0.2 0.2 0.4 0.6 0.8 1 y –1 –0.6 –0.2 0.20.40.60.8 1 x Figure for problem 8....
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This note was uploaded on 03/26/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.
 Spring '08
 Skrypka
 Math

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