Find the volume of the solid obtained by rotating the region enclosed by the curves $y=x^2 , x = 1, x = 2$, and $y=0$ about the line $x=5$

Question

Find the volume of the solid obtained by rotating the region enclosed by the curves $y=x^2, x = 1, x = 2$, and $y=0$ about the line $x=5$.

I set up the question using the cylindrical shells method. I'm not sure if I'm setting it up correctly. I graphed out the equations but I'm not sure what the radius is. I know the height is $x^2$.

$$\int_1^2 2pi(radius?)(x^2)dx$$

Answer 1

Hint Take some nice values for $x$, say $1.3, 1.5, 1.7$. How far away are each of these from the line $x=5$? Then if I just use the value $x$, how far is it away from the line $x=5$?