How do you find the volume of the solid with base region bounded by the curves #y=1-x^2# and #y=x^2-9# if cross sections perpendicular to the #x#-axis are squares?
Since the length of a square cross-section can be expressed by
the area of the cross-section can be found by
Let us find the
Since the base of the solid spans from
by using the symmetry (even function),
I hope that this was helpful.