(1 point) Compute the flux of F=xi+yj+zk through just the curved surface of the

Question

(1 point) Compute the flux of F=xi+yj+zk through just the curved surface of the cylinder x^2+y^2=16 bounded below by the plane x+y+z=1, above by the plane x+y+z=4, and oriented away from the z-axis.

Section 13.7: Problem 8 Previous Problem List Next ( 1 point) Compute the flux of F = x1+ y2+ z k through ust the curved surface of the cylinder x2 + y-16 bounded below (1 point) Compute the flux of F ri +yj + zk through just the curved surface of the cylinder r2 y2-16 bounded below by the plane x + y + 1, above by the plane x + y + z = 4, and oriented away from the z-axis flux =

Explanation / Answer

We have two surfaces:
S: z = 1 - x - y and S: z = 4 - x - y.

So, the flux s F · dS equals
s F · dS + s F · dS
= <x, y, z> · <-z_x, -z_y, 1> dA + <x, y, z> · <-z_x, -z_y, 1> dA
= <x, y, 1-x-y> · <1, 1, 1> dA + <x, y, 4-x-y> · <1, 1, 1> dA
= 1 dA + 4 dA
= 1 * (area in x^2+y^2=16) + 4 * (area in x^2+y^2=16)
= 5 * 16
= 80 .

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