Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions y=x^2 , y=8−x^2 and to the right of x=0.5 about the y-axis.
"y = x^2, y = 8 \u2212 x^2,and \\ x = 1\/2" about the y-axis.
Here is how set up the integral:
"2 \\pi \\int [-2,2] (1\/2 - x)[(8-x^2)- (x^2)]dx"
Since x=1/2 is greater than a (a= -2), I subtracted x from 1/2.
Also, since the graph of"y= 8- x^2" is above the graph of"y=x^2," Isubtracted x^2 from 8-x^2.