# Calculus 3 : Stokes' Theorem

## Example Questions

### Example Question #43 : Surface Integrals

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

Considering the integral , utilize Stokes' Theorem to determine 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

### Example Question #31 : Surface Integrals

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

Considering the integral , utilize Stokes' Theorem to determine 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

### Example Question #45 : Surface Integrals

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

Considering the integral , utilize Stokes' Theorem to determine 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

### Example Question #46 : Surface Integrals

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

Considering the integral , utilize Stokes' Theorem to determine 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

### Example Question #47 : Surface Integrals

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

Considering the integral , utilize Stokes' Theorem to determine 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

### Example Question #48 : Surface Integrals

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

Considering the integral , utilize Stokes' Theorem to determine 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

Explanation:

Explanation: