Posted by Kelly on .
The region bounded by y=x^2+1445 and y=0 is rotated about the yaxis, find the volume.

Calculus 
Steve,
The region goes from x=5 to x=9, So,
using shells,
v = ∫[5,9] 2πrh dx
where r = x and h=y
v = 2π∫[5,9] x(x^2+14x45) dx
= 448/3 π
Using discs (washers), things get a bit more complicated, because there are two branches to the parabola.
y = 4(x7)^2
x = 7±√(4y)
v = ∫[0,4] π(R^2r^2) dy
where R = 7+√(4y) and r = 7√(4y)
v = π∫[0,4] (7+√(4y))^2  (7√(4y))^2) dy
= 448/3 π