2. (10) Let F(x;y) = hy;1i and let C be the upper semicircle f(x;y) :

R2 2

x + y = 1; x 0; y 0g, oriented counterclockwise. Find the line integral

C F ds.

3. (1R0) Let F (x; y; z) = hy2z; 2xyz; xy2i and let C be the curve para- metrized by c(t) = sin2(t); cos2(t); tan2(t) for t 2 [0; =4]. Find the line integral C F ds.

4. (10) Let S be the portion of the graph of g(x;y) = 2x+2y+1 thatliesabovetherectangleR=f(x;y):0x1;0y2g. If f(x; y; z) = 2xy + z, Önd the surface integral R RS f dS.

5. (10) If S is the upper unit hemisphere, oriented with outward point- ing normal, and F (x; y; z) = tan1(x2 + y2 + z2) hy; x; zi, Önd the surface integral R RS F dS.

Subject | Mathematics |

Due By (Pacific Time) | 04/22/2014 04:00 pm |

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