- 4 30 Let S Be The Drinking Cup Which Is 4 Units Tall Whose Sides Are The Cylinder X Y 9 With Bottom At Z 0 1 (95.81 KiB) Viewed 63 times
4. (30) Let S be the drinking cup which is 4 units tall, whose sides are the cylinder x² + y² = 9, with bottom at z = 0,
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4. (30) Let S be the drinking cup which is 4 units tall, whose sides are the cylinder x² + y² = 9, with bottom at z = 0,
4. (30) Let S be the drinking cup which is 4 units tall, whose sides are the cylinder x² + y² = 9, with bottom at z = 0, and which has no top (or how would you drink?). (See picture, previous page.) Let F(x, y, z) = < −y, x,x+z>. Compute the flux of curl(F) through S. Parameterize the two pieces of S (side and bottom, see previous page for picture), compute the 2 fluxes, add, and compare to problem 3 Be sure that your normal vectors point "out". Note that your r vectors should have 2 parameters, but not the same 2 parameters. Finally, one of these integrals evaluates to 0. Just saying. curl(F) = "Sides" (cylinder shell) "Bottom" (disk)