**1.** The roof of a square floor (20π π₯ 20π) base structure can be modelled as π§(π₯, π¦) where (π₯, π¦) is the coordinate of the floor with (0,0) as the coordinate of the centre of the floor.

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**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 β A β€ π₯ β€ A and β B β€ y β€ 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 structureβs volume using the math integration method for part 1(c).

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

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