1A) Let S be the upward oriented surface of the box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane....

1A) Let S be the upward oriented surface of the box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane. That is, in the standard view, the box has a front and back, a left and right face, a top face, but no bottom face. Let F(x,y,z)=< ycos(z),zcos(x),xcos(y) >. Find the flux of curl F across S directly, without using stokes theorem.

1B) Let S be the upward oriented surface of the box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane. That is, in the standard view, the box has a front and back, a left and right face, a top face, but no bottom face \. Let F(x,y,z)= < ycos(z),zcos(x),xcos(y) >. Find the flux of curl F across S using line integrals (stokes theorem).

Solutions

Expert Solution

In 1st part solve for individual surfaces and the add them. For 2nd part, break the curve into parts and solve them.

Colby Messinger answered 1 year ago

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