Question

The mathematics department is designing some (badly needed) new furniture for its com-mons space. Some faculty have suggested making tables out of shapes of interesting graphs.One particular favorite is in the shape of the region bounded byy= sin(x2) and thex-axisbetweenx= 0 andx=√π. There are two competing designs for the table. Design A usesa thickness of 1 inch everywhere on the table. The more artistic Design B employs a slightwedge shape underneath the table, with thickness 1 +x√π20inches. Each table balances ona single leg. Should the leg for design A be to the left of, to the right of, or have the samex-coordinate as the leg for design B? Explain your answer in a sentence or two. Note thatyou arenotasked to actually compute the centers of mass.

Answer 1