CPM Homework Help : APCALC Problem 8-110

Given that a typical cross-section of a solid taken perpendicular to the $x$ -axis has an area of $A(x) = \ln(x)$ , set up an integral to calculate the volume of this solid from $[a, b]$ . Does it matter what the shape of the solid is? Explain.

Hint:

$\text{volume by cross-sections }= \int_{a}^{b}(\text{area})dx$

Of course every shape has a different area function, and this $\text{area function}= \ln(x)$ .
It is not possible to know what the cross-sections looks like. Perhaps they are rectangles with $\text{height} = \ln(x)$ and $\text{base} = 1$ ? But, they could also be strange looking shapes. As long as all of their $\text{areas} =\text{(coefficient)(base)(height)} = \ln(x)$ , the volume by cross-section formula will work.