Question

Rotate the region bounded by the given curves about the given line and find the volume resulting solid.
x=1+y^2 and the xaxis from x=1 to x=5 about y=3

Answer 1

we need the function in terms of x, solving for y
y = sqrt(x-1)
outer radius(R) = 3
inner radius(r) = 3-sqrt(x-1)
\[V = \pi \int\limits_{1}^{5}3^{2} -(3-\sqrt{x-1})^{2} dx\]