Question

Determine the volume of the solid obtained by rotating the region bounded by y= x^2-4x+5 at x=1, x= 4 and the x-axis about the x-axis.

Answer 1

Using disc method , sum up areas of each circular cross-section
\[V = \pi \int\limits R^2 dx\]
radius = y-value
\[V=\pi \int\limits_1^4 (x^2 -4x+5)^2 dx\]