### All Calculus 3 Resources

## Example Questions

### Example Question #1 : 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:

**Possible Answers:**

**Correct answer:**

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 **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #2 : 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:

**Possible Answers:**

**Correct answer:**

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 **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #3 : 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:

**Possible Answers:**

**Correct answer:**

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 **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #4 : 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:

**Possible Answers:**

**Correct answer:**

In order to utilize Stokes' theorem, note its form

**F** over an oriented surface **S** is equivalent to the function **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #5 : 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:

**Possible Answers:**

**Correct answer:**

In order to utilize Stokes' theorem, note its form

**F** over an oriented surface **S** is equivalent to the function **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #6 : 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:

**Possible Answers:**

**Correct answer:**

In order to utilize Stokes' theorem, note its form

**F** over an oriented surface **S** is equivalent to the function **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #7 : 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:

**Possible Answers:**

**Correct answer:**

In order to utilize Stokes' theorem, note its form

**F** over an oriented surface **S** is equivalent to the function **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #8 : 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:

**Possible Answers:**

**Correct answer:**

In order to utilize Stokes' theorem, note its form

**F** over an oriented surface **S** is equivalent to the function **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #9 : 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:

**Possible Answers:**

**Correct answer:**

In order to utilize Stokes' theorem, note its form

**F** over an oriented surface **S** is equivalent to the function **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral

### Example Question #10 : 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:

**Possible Answers:**

**Correct answer:**

In order to utilize Stokes' theorem, note its form

**F** over an oriented surface **S** is equivalent to the function **F **itself integrated over the boundary curve, **C**, of **S**.

Note that

From what we're told

Meaning that

From this we can derive our curl vectors

This allows us to set up our surface integral