The area (in sq. units) of the part of the circle x 2 + y 2 = 36 , which is outside the parabola y 2 = 9 x , is equal to

Step-by-step solution

Required area = π × 6 2 - 2 ∫ 0 3 9 x d x + ∫ 3 6 36 - x 2 d x = 36 π - 6 x 3 / 2 3 / 2 0 3 - 2 x 2 36 - x 2 + 18 sin - 1 x 6 3 6 = 36 π - 12 3 - 2 0 - 9 3 2 + 9 π - 3 π = 24 π - 3 3   sq . units