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 k around the curve c: the ellipse 16x squared plus 4 y squared equals 3 in the xy-plane, counterclockwise when viewed from above.

The circulation of the field f(x) over curve C is Zero

Step-by-step explanation:

The function and curve C is ellipse of equation

Theory: Stokes Theorem is given by:

Where, Curl f(x) =

Also, f(x) = (F1,F2,F3)

Using Stokes Theorem,

Surface is given by g(x) =

Therefore, tex]\hat{N} = grad(g(x))[/tex]

Now,  

Curl f(x) =

Curl f(x) =

Curl f(x) = (0,0,4)

Putting all values in Stokes Theorem,

I=0

Thus, The circulation of the field f(x) over curve C is Zero

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step-by-step explanation:

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