Question

Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + 7 k S is the boundary of the region enclosed by the cylinder x^2 + z^2 = 1 and the planes y=0 and x+y = 2.

Answer 1

sounds delightful ... there are certain parts we should work on getting right? gradient and the ds

Answer 2

\[\int\hspace{-.6em}\int\limits_{S}~F\cdot dS=\int\hspace{-.6em}\int\limits_{S}~F\cdot n~ dS\]

Answer 3

iv'e converted the orginal equations to cylidrical but can figurre out what to put as \[r(\theta,y)=?\] the equation i am using to solve is \[\int\limits_{}^{}\int\limits_{}F(r(\theta,y))\times(r \theta X ry)\]

Answer 4

\[F(r(\theta,y))=\cos(\theta)i+yj+9k\]

Answer 5

F(x, y, z) = x i + y j + 7 k S is the boundary of the region enclosed by the cylinder x^2 + z^2 = 1 and the planes y=0 and x+y = 2.



that was a pain to try to draw out on here lol