In this section of the lab, we will estimate the area enclosed by the walls of our Metrodome model. Naturally, our answers will depend on our mathematical model.

- Set up an iterated integral for the area of the rectangle satisfying
and .
- Although the integral is trivial to solve by hand, let's gain
experience using Maple to compute
a double integral for the area:

`int( int(1, y=-1..1), x=-6/5..6/5);` - Why is the integrand of the previous integral equal to 1?

A different model for the stadium is to assume the walls of the Metrodome
are given by an ellipse with axes of length and **1**.

- Set up an iterated integral for the area of the ellipse and
compute the integral to find the are of the ellipse. Hint: to
prevent ``parenthesis mismatch,'' define
`M := sqrt(1-(5*x/6)^2);`

and use a domain of integration that looks like`y=-M..M, x=-6/5..6/5`. - Compute the integral to find the area of the ellipse.

A more sophisticated model postulates that the walls of the stadium satisfy the equation

- Set up an iterated integral for the area enclosed by this curve.
- Compute the integral to find the area. Hint:
`Maple`will be unable to symbolically solve the integral. Use the`evalf`command to evaluate the integral numerically.

- What is the scale factor in this problem (
*i.e.*, 1 unit is how many feet)? Use this to estimate the area enclosed by the walls of the real Metrodome. - Do some models definitely over- or under-estimate the area? Why?

Thu Feb 20 09:21:36 CST 1997