# Calculus 3 : Stokes' Theorem

## Example Questions

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### Example Question #81 : Surface Integrals

Let S be a known surface with a boundary curve, C.

Considering the integral , utilize Stokes' Theorem to determine for an equivalent integral of the form:       Explanation:

In order to utilize Stokes' theorem, note its form The curl of a vector function F over an oriented surface S is equivalent to the function itself integrated over the boundary curve, C, of S.

Note that From what we're told And it can be inferred from this that   A helpful approach can be to look at the right sides of the equations and see what variables are represented compared to what variables a vector component of F is being derived for. Doing this and integrating, we can infer that and ### Example Question #81 : Stokes' Theorem

Let S be a known surface with a boundary curve, C.

Considering the integral , utilize Stokes' Theorem to determine for an equivalent integral of the form:       Explanation:

In order to utilize Stokes' theorem, note its form The curl of a vector function F over an oriented surface S is equivalent to the function itself integrated over the boundary curve, C, of S.

Note that From what we're told And it can be inferred from this that   A helpful approach can be to look at the right sides of the equations and see what variables are represented compared to what variables a vector component of F is being derived for. Doing this and integrating, we can infer that and ### Example Question #81 : Surface Integrals

Let S be a known surface with a boundary curve, C.

Considering the integral , utilize Stokes' Theorem to determine for an equivalent integral of the form:       Explanation:

In order to utilize Stokes' theorem, note its form The curl of a vector function F over an oriented surface S is equivalent to the function itself integrated over the boundary curve, C, of S.

Note that From what we're told And it can be inferred from this that   A helpful approach can be to look at the right sides of the equations and see what variables are represented compared to what variables a vector component of F is being derived for. Doing this and integrating, we can infer that and ### Example Question #84 : Stokes' Theorem

Let S be a known surface with a boundary curve, C.

Considering the integral , utilize Stokes' Theorem to determine for an equivalent integral of the form:       Explanation:

In order to utilize Stokes' theorem, note its form The curl of a vector function F over an oriented surface S is equivalent to the function itself integrated over the boundary curve, C, of S.

Note that From what we're told And it can be inferred from this that   A helpful approach can be to look at the right sides of the equations and see what variables are represented compared to what variables a vector component of F is being derived for. Doing this and integrating, we can infer that and 1 2 3 4 5 6 7 9 Next →

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