Find the volume of the solid generated by rotating the region 0<y<5-x^2 about the x-axis

Answer 1

the volume would be

∫[-√5,√5] πr^2 dx
where r=y=(5-x^2)
Because of symmetry, that is
2∫[0,√5] π(5-x^2)^2 dx = 80π√5/3

using shells, that is
2∫[0,5] 2πrh dy
where r=y and h=x=√(5-y)
2∫[0,5] 2πy√(5-y) dy = 80π√5/3