Notes

Civil engineering application of Simpson's Rule to centroids
Building a highway going through a town
Cross-sectional design of highway - arc length, volume, centroids
Design of highway: top X rectangle is asphalt, bottom X rectangle plus cut-out half-circle is concrete, coord system has split down middle
Curve design is a piecewise curve. Given a set of formulas.
Use Simpson's Rule to compute the x and y centroids of the highway shape (Figure). Assume density of materials is same and is 2400 kg/m3.
Use Simpson's Rule to compute the arc length of the road, and report the total length in ft.
Highway standards require a minimum lane width of 15 feet, 10 feet for side shoulder, 5 feet for inner shoulder, 3 lanes both directions. Total width of X.
Use Simpson's Rule to find the total volume of asphalt, volume of concrete required (use Pappus' Theorem to obtain the volume via V = A * length traveled)

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