**2. **There is a shape at the centre of the structure from the floor to the roof. Below is the position of the x and y coordinates.

**(a)** Present the shape by joining all points in FOUR straight lines and ONE quarter-circle.

**(b)** Write down the equation for the FOUR straight lines and ONE quarter-circle.

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**Wolfram Alpha Method**

**(c)** Double Integral

Determine the value of the upper and lower limits of x1, x2, y1, and y2. Find the volume of the pillar and explain the working steps.

**(d) Change Order of Double Integral**

Determine the value of the upper and lower limits of x3, x4, y3, and y4. Find the volume of the pillar and explain the working steps.

**MATLAB or OCTAVE Method**

**(e)** Find the pillar volume by using MATLAB or OCTAVE (integral2 function). Use those limits stated in part 2(c).

**(f)** Comments on the results for part 2(c), 2(d), and 2(e).

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