The area bounded by y + x 2 ≤ 4 x and y ≥ 3 is k sq.units, then 3 k is equal to

Step-by-step solution

Solving, y = - x 2 + 4 x and y = 3 , we get, x = 1 , 3 ∴ A is 1 , 3 and B is 3 , 3 Hence, the required area is k = ∫ 1 3 - x 2 + 4 x - 3 d x = - x 3 3 + 2 x 2 - 3 x 1 3 = - 1 3 27 - 1 + 2 9 - 1 - 3 3 - 1 = - 26 3 + 16 - 6 = 4 3 sq. units ⇒ 3 k = 4