Change of Variables

Help Questions

Multivariable Calculus › Change of Variables

Questions 1 - 3
1

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

using the transformation , and .

Explanation

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.

2

Convert the following into spherical coordinates.

Explanation

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

Now lets apply this to our problem.

3

Convert the following into spherical coordinates.











Explanation

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

Now lets apply this to our problem.

Return to subject