Let R be the region bounded by y = x and y = x2. Write an integral expression for the volume of the solid with base R
whose slices perpendicular to the y-axis are squares
R is this region:
We're slicing the same way as in (1), but now instead of the slice at position y being a semi-circle with diameter , it's a square with side-length .
The volume of the slice at position y is
Since y still goes from 0 to 1, the volume of the whole solid is