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(solution) Math 327-01 Problem Set 08 (Week 13)-Find the surface area of the portion of the paraboloid


Math 327-01 Problem Set 08 (Week 13) Due May 6, 2016 Name: (© 03/07/2016 Author: Dale M. Rohm) Complete the following problems on your own paper and staple this sheet to the front as a cover page. Show all work neatly and completely in order to ensure full and partial credit. I will deduct points for sloppy or incomplete work. Treat these problems as you would any homework problem set, you may work together and seek help. 1. Find the surface area of the portion of the paraboloid D œ #B# +#C# that lies between the planes D œ # and D œ ) . 2. Evaluate the surface integral ( ( CD .W where D is the triangular portion of the plane D B C D œ " that lies in the first octant. 3. Evaluate the surface integral ( ( È% D .W where D is the portion of the cylinder D B# C# œ * with ! Ÿ D Ÿ & Þ 4. Evaluate the flux integral ( ( aCß Bß D b † R .W where R is the upward pointing unit D vector to the paraboloid D œ " B# C# where ! Ÿ D Ÿ " Þ 5. Evaluate the flux integral ( ( aBß Dß Cb † R .W where R is the upward pointing D unit vector to the hemisphere B# C# D # œ % where ! Ÿ D Ÿ # Þ

 


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