The region *R* looks like (a) When *R* is rotated around the *x*-axis we get the solid A slice perpendicular to the *x*-axis is a washer. The radius of the washer is *x* and the radius of its hole is *x*^{2}. This means the area of the side of the washer is π(*r*_{outer})^{2} – π(*r*_{inner})^{2} = π(*x*)^{2}-π(*x*^{2})^{2} = π[*x*^{2 }– *x*^{4}]. The volume of the washer is π[*x*^{2} – *x*^{4}] Δ *x*. Since *x* goes from 0 to 1 in this region, the volume of the solid is (b) Rotating *R* around the *y*-axis gives us the solid A slice perpendicular to the *y*-axis is a washer with inner radius *y* and outer radius . The area of the side of the washer is and the volume of the washer is π[*y* – *y*^{2}] Δ *y*. Since *y* goes from 0 to 1 in the region *R*, the volume of the solid is |