Question

-. (15 pts.) Let S is the first-octant portion of the plane 2x + y +z = 4. Evaluate the surface integral SSE (2y2 + 2yz) ds.
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Solution:

Given that: The first-octant portion of the plane is, 20+ y +2=4 Evaluate the surface integral, Sfg cay²+24 z) db Here, 2x+y+ss 4-0 4:0 4-25 6 => 56 4-23 23 Cy?? 4-23 dx NOW, SS (2y²+2y =) db 4-20 so Czy²+2y c4-ex-y) dy doc => 68 & cay-uzy) dy dx Sf4

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