Unformatted text preview: surface with boundary C . (a) Find the values of the constants α and β so that the flux of F through σ has the same value for any choice of σ . (b) For these special values of the constants α and β , calculate the flux . ∫∫ ⋅ σ S F d [Hint: Pick a convenient σ .] 3. The base of a solid (of constant density) is the disk 25 2 2 ≤ + y x in the plane z = 4. The solid has volume V = 60 and its centroid is located at (2, 1, 10). Consider the vector field given by . ) ( ) ( ) ( 2 2 3 3 1 2 k j i F z y x yz e x x yz + +-+ + + = Find the flux of F (a) outward through the surface of the solid; (b) through the surface of the solid excluding the base. [Hint: the centroid of a solid occupying region R of volume V is given by .] , , 1 ) , , ( = ∫∫∫ ∫∫∫ ∫∫∫ R R R zdV ydV xdV V z y x...
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- Spring '10
- Vector Calculus, 50 Minutes, R R R