Unformatted text preview: + 2z = 2 in the ﬁrst octant: 1 3.
Use Stoke’s Theorem to evaluate ´ C F · dr where 1
F (x, y, z ) = x2 y i + x3 j + xy k
3 and C is the curve of intersection of the hyperbolic paraboloid z = y 2 − x2 and the cylinder x2 + y 2 = 1,
oriented counterclockwise as viewed from above. Here are 2 diﬀerent views of the curve in question: 4.
Evaluate ´ C F · dr where F is the vector ﬁeld given by
F (x, y, z ) = (y + sin x) i + z 2 + cos y j + x3 k and C is the curve r (t) = sin (t) i + cos (t) j + sin (2t) k. [Hint: Observe that C lies on the surface z = xy ]. 2...
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This note was uploaded on 02/12/2014 for the course MATH 2233 taught by Professor Suagee during the Summer '13 term at GWU.
 Summer '13
 Suagee
 Multivariable Calculus

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