### All Multivariable Calculus Resources

## Example Questions

### Example Question #12 : Multivariable Calculus

Convert the following into spherical coordinates.

**Possible Answers:**

**Correct answer:**

In order to convert to spherical coordinates , we need to remember the conversion equations.

Now lets apply this to our problem.

### Example Question #13 : Multivariable Calculus

Evaluate , where is the trapezoidal region with vertices given by , , , and ,

using the transformation , and .

**Possible Answers:**

**Correct answer:**

The first thing we have to do is figure out the general equations for the lines that create the trapezoid.

Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.

So our region is a rectangle given by ,

Next we need to calculate the Jacobian.

Now we can put the integral together.

### Example Question #1 : Change Of Variables

Convert the following into spherical coordinates.

**Possible Answers:**

**Correct answer:**

In order to convert to spherical coordinates , we need to remember the conversion equations.

Now lets apply this to our problem.

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