Let D be the region between the parabolas y = x 2 +1 and y = 3−x 2 where |x| ≤ 1. (a) Find a horizontal line y = C such that D is symmetric with respect to this line. (b) Use Pappus’ Centroid Theorem...

Let D be the region between the parabolas y = x²+1 and y = 3−x²

where |x| ≤ 1.
(a) Find a horizontal line y = C such that D is symmetric with respect to this line.

(b) Use Pappus’ Centroid Theorem to find the volume for the solid of revolution obtained by rotating D around the x-axis.

Answer part b of this question