The manufacturer of glass for a window in a conversion van needs to approximate its center of mass. A coordinate system is superimposed on a prototype of the glass (see figure). The measurements (in centimeters) for the right half of the symmetric piece of glass are listed in the table.

(a) Use Simpson’s Rule to approximate the center of mass of the glass.
(b) Use the regression capabilities of a graphing utility to find a fourth-degree polynomial model for the data.
(c) Use the integration capabilities of a graphing utility and the model to approximate the center of mass of the glass. Compare with the result in part (a).

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