Text Compute the area of the region between the parabolas y=8−x2y=8-x^{2}y=8−x2 and y=x2y=x^{2}y=x2. Solution Intersections: 8−x2=x2⇒x=±28-x^{2}=x^{2}\Rightarrow x=\pm28−x2=x2⇒x=±2. The upper curve is y=8−x2y=8-x^{2}y=8−x2. A=∫−22(8−2x2)dx=[8x−2x33]−22=643≈21.333A=\displaystyle\int_{-2}^{2}(8-2x^{2})dx=\Big[8x-\tfrac{2x^{3}}{3}\Big]_{-2}^{2}=\dfrac{64}{3}\approx21.333A=∫−22(8−2x2)dx=[8x−32x3]−22=364≈21.333. A=643≈21.333\boxed{A=\tfrac{64}{3}\approx21.333}A=364≈21.333