Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.

Question

x + y = 3, x = 4 − (y − 1)^2

Answer 1

the curves intersect at y=0,3 so the volume is

v = ∫ 2πrh dy
where r=y and h=4-(y-1)^2 - (3-y)
v = ∫[0,3] 2πy(4-(y-1)^2 - (3-y)) dy = 27π/2

Answer 2

yoop

Answer 3

Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.
x = 30y2 − 6y3, x = 0