If the area bounded by the curve 2 y 2 = 3 x , lines x + y = 3 , y = 0 and outside the circle x - 3 2 + y 2 = 2 is A, then 4 π + 4 A is equal to __________.

Step-by-step solution

Given: 2 y 2 = 3 x ,   x + y = 3 slope   is   - 1   &   x - 3 2 + y 2 = 2 Now plotting the diagram of the above function we have, So, required area is A = ∫ 0 3 2 3 - y - 2 y 2 3 d y - π 2 2 × 45 ° 360 ° ⇒ A = 3 y - y 2 2 0 3 2 - 2 3 y 3 3 0 3 2 - π 4 ⇒ A = 21 8 - π 4 So, A = 1 4 21 2 - π ⇒ π + 4 A = 21 2 ⇒ 4 π + 4 A = 42