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:

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)