Area

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?