Use the surface integral in Stokes' Theorem to calculate the circulation of the field Bold Upper F equals x squared Bold i plus 4 x Bold j plus z squared Bold kF=x2i+4xj+z2k around the curve C: the ellipse 25 x squared plus 16 y squared equals 525x2+16y2=5 in the xy-plane, counterclockwise when viewed from above.

Stokes' theorem says the integral of the curl of over a surface with boundary is equal to the integral of along the boundary. In other words, the flux of the curl of the vector field is equal to the circulation of the field, such that

We have

Parameterize the ellipse by

with and .

Take the normal vector to to be

Then the flux of the curl is

c

step-by-step explanation:

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