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 + z⁴ k

S is the part of the cone z =

x2 + y2

beneath the plane

z = 1

with downward orientation

Answer 1

Dear student,

Here the question is not that much clear that which flux has to be calculated.(i.e through cone only or both cone and upper surface) That's why I have calculated flux through all the surfaces.you may consider what you want.

Feel free to ask doubts in the comments section.

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