Question

Find the volume of the solid obtained by rotating about the x-axis
the region bounded by the curve y =sqrt(x-1) and the x-axis between x = 2 and x = 5 .

Answer 1

\[
\int_2^5 \pi y^2 dy
\]
It should be easy now. Replace y by its value and integrate.

Answer 2

Use disc method~
\[volume = \pi \int_{2}^{5} \sqrt{x-1} ^2 dx =\pi \int_{2}^{5} (x-1)dx \]
I bet you can solve it from here :)