Mathematics

Problem

Which of the following definite integrals gives the volume of the solid whose base is the region bounded by the lines

y=x

and

y=4-x

for

0\le x\le2

, if cross sections perpendicular to the

x

-axis are equilateral triangles? a)

\displaystyle \int_{0}^{2}\frac{\pi}{8}\,(4-2x)^2\,dx

\displaystyle \int_{0}^{2}\frac{\sqrt3}{4}\,(4-2x)\,dx

\displaystyle \int_{0}^{2}\frac{\sqrt3}{4}\,(4-2x)^2\,dx

\displaystyle \int_{0}^{2}\frac{\sqrt3}{4}\,(4-x)^2\,dx