Answer to Question #247250 in Chemical Engineering for Thando

Question

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.

Answer 1

$y = x^2, y = 8 − x^2,and \ x = 1/2$ 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.