The area (in square units) of the region bounded by the parabola y 2 = 4 ( x - 2 ) and the line y = 2 x - 8 .

Step-by-step solution

Given curve is y 2 = 4 x - 2 and line y = 2 x - 8 Finding the point of intersection of y = 2 x - 4 and y 2 = 4 x . ⇒ x = y + 8 2 = y 2 + 8 4 ⇒ 2 y + 16 = y 2 + 8 ⇒ y 2 - 2 y - 8 = 0 ⇒ y - 4 y + 2 = 0 ⇒ y = 4 , - 2 ⇒ x = 6 , 3 Area of the bounded region is given by, A = ∫ - 2 4 y + 8 2 - y 2 4 + 2 d y ⇒ A = y 2 4 + 2 y - y 3 12 - 2 4 ⇒ A = 4 + 8 - 16 3 - 1 + 4 - 2 3 ⇒ A = 9 sq . units .