Chapter 8.6, Problem 72E

Building DesignThe cross section of a precast concrete beam for a building is bounded by the graphs of the equations

$x=\frac{2}{\sqrt{1+y^2}},x=\frac{-2}{\sqrt{1+y^2}},y=0,\text{ and }y=3$

where x and y are measured in feet. The length of the beam is 20 feet (see figure).

(a) Find the volume V and the weight W of the beam. Assume the concrete weighs 148 pounds per cubic foot.

(b) Find the centroid of a cross section of the beam.