$\"\"$

\

Work done by force $\"\"$ in moving a particle along the path $\"\"$ is $\"\"$ .

\

Stokes theorem:

\

$\"\"$ .

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The function is $\"\"$ .

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If $\"\"$ then $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Find the plane equation, for points $\"\"$ and $\"\"$ .

\

Let the equation of the plane is $\"\"$ .

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The point $\"\"$ on the plane is $\"\"$

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$\"\"$ .

\

The point $\"\"$ on the plane is $\"\"$ .

\

$\"\"$

\

$\"\"$

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The point $\"\"$ on the plane is $\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ , $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in above expression.

\

$\"\"$

\

$\"\"$

\

The plane equation is $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Where $\"\"$ , $\"\"$ is the projection of the surface on the $\"\"$ plane and $\"\"$ is the plane equation.

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in above expression.

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ is the projection of the surface $\"\"$ on the $\"\"$ plane.

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$\"\"$ is the region inside the points $\"\"$ and $\"\"$ .

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From the points $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

The work done is $\"\"$ .

\

$\"\"$

\

The work done is $\"\"$ .