Let E denote the solid cylinder bounded by x2 + y2 = 4, z = 0 and z = 3. Let F(x,y,z) = (x3 + tan(yz))i + (y3 - exz)j + (3z + x3)k. Evaluate [image]

Suppose F = (y + 2x, 7x + 4z, 6y + 2x) and S is a surface bounded by C, a circle with radius 3, center at (2, 0, 0), in the plane x = 2, and oriented counterclockwise as viewed from the origin (0, 0, 0). Find the flux of curl(F) across S and then evaluate the circulation & F. dr. (Use symbolic notation and fractions where needed.) DS Incorrect JC curl(F). dS = F. dr = 18T Incorrect 18A

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Let w = x" dz A dx + (y° + x°) dx ^ dy be a two-form on R³. Determine the one-form *d(*w), where * is the Hodge star operator in IR°. dz dx + |dy+ *d(*w)