Volume of a region R when revolved about the x-axis

Question

Find the volume of the region when revolved about the $x$ axis

$y= \sqrt{x-1}$, $y=2$, $y=0$, and $x=0$

Is this right?

Also if you could help me with revolving this same region around $y=2$, and $x=5$, I would really appreciate it.

NOTE: The y=2, and x=5 are two separate questions, so in 1 question asked to revolve about y=2, and in the other anoe about x=5

Answer 1

Based on the problem and the graph you presented, your volume integral formula may be more like this: $$V=\int_0^1 \pi (2)^2 \, dx+\int_1^5 \pi(2)^2-\pi(\sqrt{x-1})^2 \, dx$$