I think you meant 9 for the denominator in the term...for you were originally dividing by zero...

First, solve for y:

Since we are told to find the area under the ellipse in the first quadrant, we take

Now, we are to use a midpoint Riemann Sum:

We are told that , and the ellipse's major axis is along the x-axis and has a length of 4 units. Thus, we are applying the Riemann sum over the interval .

What is the midpoint of each section?

Our midpoint x values are

So our Riemann sum can be expressed as . Evaluating, we see that we have:

Thus, the total area would be 4 times this amount.

Does this make sense?

--Chris