Text Compute the area of the region between the parabola y=x2y=x^{2}y=x2 and the line y=4x−3y=4x-3y=4x−3. Solution Intersections: x2=4x−3⇒x=1, x=3x^{2}=4x-3\Rightarrow x=1,\ x=3x2=4x−3⇒x=1, x=3. The line is above. A=∫13[(4x−3)−x2]dx=[2x2−3x−x33]13=43≈1.333A=\displaystyle\int_1^3\big[(4x-3)-x^{2}\big]dx=\Big[2x^{2}-3x-\tfrac{x^{3}}{3}\Big]_1^3=\dfrac43\approx1.333A=∫13[(4x−3)−x2]dx=[2x2−3x−3x3]13=34≈1.333. A=43≈1.333\boxed{A=\tfrac43\approx1.333}A=34≈1.333