The area (in sq. units) of the region enclosed between the parabola y 2 = 2 x and the line x + y = 4 is ______.

Step-by-step solution

y 2 = 2 x   ⇒ y 2 = 2 4 - y ⇒ y 2 + 2 y - 8 = 0     ⇒ y = - 4 , 2 The point of intersection of y 2 = 2 x and x + y = 4 are 8 , - 4 and 2 , 2 Area = ∫ - 4 2 4 - y - y 2 2 d y   = 4 y - y 2 2 - y 3 6 - 4 2 = 8 - 2 - 4 3 - - 16 - 8 + 32 3 = 54 3 = 18 Sq.units.