Let α be the area of the larger region bounded by the curve y 2 = 8 x and the lines y = x and x = 2 , which lies in the first quadrant. Then the value of 3 α is equal to

Step-by-step solution

We have, y 2 = 8 x y = x Point of intersection of curve and a line is A 8 , 8 . Required area α = ∫ 2 8 8 x - x d x ⇒ α = 4 2 x 3 2 3 - x 2 2 2 8 ⇒ α = 4 2 2 2 3 3 - 64 2 - 4 2 2 3 3 - 4 2 ⇒ α = 112 3 - 30 ⇒ α = 22 3 So, 3 α = 22