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Numerical Area

As in the first part of this lab, we will use an ellipse with axes 6/5 and 1 as our basic example.

QUESTION 6: If you have not already done so, define
`M := sqrt(1-(5*x/6)^2);`
then issue the special Maple command:
gridplot2d(x=-2..2,y=-1..1, grid=[10,10],region=-M..M); (Hint: you may want to ``constrain'' the resulting image so that the horizontal and vertical scales are the same.)
• Use the displayed grid to compute a lower bound on the area of the indicated ellipse. Explain what method you used to approximate the area.
• Compute an upper bound for the area. Again, explain your method.
• Sketch a picture (use 2 colors!) indicating the geometry behind your two answers.

QUESTION 7: The special Maple command leftbox2d computes the area by adding up the area of all boxes in a grid whose lower left corner is contained in a region.

• Compute an approximation to the area of the previous ellipse by using the command
leftbox2d( 1, x=-2..2,y=-1..1, grid=[10,10], region=-M..M);
• Try to determine if this method of approximation produce an upper bound or a lower bound for the area of the ellipse. Again, illustrate your answer with a picture.

Bob Hesse
Thu Feb 20 09:21:36 CST 1997