The base of a solid is the region bounded by the graph of y= (x^2) and the line y=1. Each cross section perpendicular to the y axis is a square. What is the volume of the solid?
How do we know which way to slice? Do i have to get the answer and times it by two because it includes both quadrant one and two?
Thank you
If you integrate in the direction of the y axis, your limits of integration become 0 and 1, and the differential volume element is given by $dV = (2x)^2dy$. Since $y = \sqrt{x}$, the integral can be written $\int^1_0 4ydy$