1. The roof of a square floor (20𝑚 𝑥 20𝑚) base structure can be modeled as 𝑧(𝑥, 𝑦) where (𝑥, 𝑦) is the coordinate of the floor with (0,0) as the coordinate of the center of the floor.

Wolfram Alpha Method
(a) Write down the selection of function z(x, y) according to the input
variables of A and B.
(b) To show the 3D graph of the roof, the function z(x, y) above the floor region − A ≤ 𝑥 ≤ A and − B ≤ y ≤ B
(c) Double Integral
Determine the value of the upper and lower limits of a, b, c, and d. Calculate the volume of the structure by using double integrals.

(d) Change Order of Double Integral
Determine the value of the upper and lower limits of e, f, g, and h.
Calculate the volume of the structure by using both double integrals.

Math Integration Method
(e) Determine the structure’s volume using the math integration method for part 1(c).

(f) Comments on the results for parts 1(c), 1(d) and 1(e).