Hello, nmq3b!
Find the volume of the solid formed by revolving fhe region in quadrant 2,
bounded above the curve $\displaystyle y \,=\,x^3$, below by the xaxis,
and on the left by the line $\displaystyle x = 1$, about the line $\displaystyle x = 2$ Code:
: * 
: 
: * 
: * 
: ::* 
: :::::*. 
 +     +     *      
2 1  *
:  *
:  *

"Shells" formula: .$\displaystyle V \;=\;2\pi\int^b_a\text{(radius)(height)}\,dx$
We have: .$\displaystyle \text{radius} = x + 2,\;\text{height} = x^3$
Hence: .$\displaystyle V \;=\;2\pi\int^0_{\text{}1}(x+2)(x^3)\,dx \;=\;2\pi\int^0_{\text{}1}(x^4 + 2x^3)\,dx $