### Home > APCALC > Chapter 12 > Lesson 12.1.4 > Problem12-43

12-43.

Set up an integral to represent the volume of the solid formed by semicircular cross-sections that are perpendicular to the $x$-axis with a base bounded by $y = e^{x}$ and $y = -2^{x}$ over the interval $[0, 4]$.

Since $e^x > -2^x$ for all $x$, the diameter of the base will be $(e^x - (-2x))$.

For a semicircular region, $A = 0.5πr^2$.

$\int_0^4 0.5\pi\Big(\frac{d}{2}\Big)^2dx$