Let S be the surface that is bounded on the left by the hemisphere x 2 y 2 z 2 a 2 , y 0, in the middle by the cylinder x 2 z 2 a 2 , 0 y a, and on the right by the plane y a Find the flux of F yi zj xk outward across S

Question: Let S be the surface that is bounded on the left by the hemisphere x 2 + y 2 + z 2 = a 2

Let S be the surface that is bounded on the left by the hemisphere x² + y² + z² = a², y ≤ 0, in the middle by the cylinder x² + z² = a², 0 ≤ y ≤ a, and on the right by the plane y = a. Find the flux of F = yi + zj + xk outward across S.

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