Question

The region bounded by the curve y=x^2+1 and the line y=-x+3 is revolved around the line y=5 to generate a solid. Find the volume of that solid

Answer 1

Find volume using disc or washer method
each cross-section is a ring with inner area and outer area
the inner radius is 5-f(x) or 5-(-x+3) = x+2
outer radius is 5-g(x) or 5-(x^2 +1) = 4-x^2
\[V = \pi \int\limits_{-2}^{1}(4-x^{2})^{2} - (x+2)^{2} dx\]