This problem illustrates the case when the vector field is not constant and the

Question

This problem illustrates the case when the vector field is not constant and the surface is parallel to one of the coordinate planes. Let F^rightarrow = (x+y-4)i^rightarrow. Let S be the triangle as shown, oriented away from the origin. Which of the following would be appropriate for dA^rightarrow in this case? dA^rightarrow = 5 i^rightarrow dA dA^rightarrow = -i^rightarrow dA dA^rightarrow = - i^rightarrow dA dA^rightarrow = 8^i^rightarrow dA After computing F^rightarrow mid dot dA^rightarrow, set up the iterated integral that is needed to find flux. Integral_ ___________^__________ integral _ ___________^___________ (___________)dzdy Evaluate your integral to find flux. Integral _s F^rightarrow middot dA^rightarrow = ________________

Explanation / Answer

dA = - idA

flux = double integral( F.n )ds

(y = 0to 2 )(z=0 to 8-4y)(x+y-4)i .(-i).(-i) dA

(y = 0to 2 )(z=0 to 8-4y(5+y-4) dzdy

(y = 0to 2 )(z=0 to 8-4y(1+y) dzdy

(y = 0to 2 )(8+4y-4y^2)dy

=40/3

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