# 201MS There is a shape at the centre of the structure from the floor to the roof: Engineering Mathematics 2 Assignment, CU

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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