The base of a solid consists of the region bounded by the parabola y=rootx, the line x=1 and the x-axis. Each cross section perpendicular to the base and the x-axis is a square. Find the volume of the solid.

Answer 1

Each cross section (from x=0 to x=1) is a square of side √x.

So the total volume is the area of the square times dx, or A(x)dx

V=∫ (√x)^2dx from x=0 to 1
=∫ xdx
=[x²/2] from 0 to 1
= 1/2