Cooling towers at nuclear power plants have a "pinched" chimney shape (which promotes cooling within the tower) formed by rotating a hyperbola around an axis. The following function, where x and y are in feet, describes the shape of such a tower (laying on its side). Determine the volume of the tower by rotating the region bounded by the graph of y about the x-axis. x2 y = 60 1+ 21,000 . for - 200 Exs 100, For a continuous function f defined on [a, b], the volume, V, of the solid of revolution obtained by rotating the area under the graph of f from a to b about the x-axis is given by the integral below. Use this formula to find the volume of the tower by rotating the region under the graph of y = 60 /1+ = 21,000 - from x= - 200 to x = 100 about the x-axis. 100 V = * 60 1+ dx Substitute into the equation. 21,000 - 200 100 = [ * 602 1 +7 x2 21,000 dx Simplify the integrand. - 200 100 = 3600m 1 + dx 21,000 Evaluate 60- and factor out the constants. - 200 100 3 = 3600x X + - Integrate. 63,000 200 Evaluate the integral, rounding to the nearest whole number. 100 V = 3600x X+ 63,000 - 200 = 3600x 100 + 1003 -200 + (-20013 Evaluate the integral. 63,000 63,000 ~5,008,596 Simplify. Therefore, the volume is 5,008,596 At3