Volume of a solid in first quadrant

[Ashford]

Homework Statement

Find the volume of the solid whose base is the region in the first quadrant bounded by the curves y=x^2 and y=x, and whose cross sections perpendicular to the x-axis are squares.



No idea what to do here

 

[Mark44]

Start by drawing a graph of the region. Then draw a sketch of the solid object.

 

[Ashford]

Ok, I've done that but I still don't know which equation to use and how to set it up.

 

[Mark44]

Your typical volume element has a base that extends from y = x^2 up to y = x, has the same height, and is $\Delta x$ wide. Your limits of integration are the values of x where the two curves intersect.