Let A be the area of the region ( x , y ) : y ≥ x 2 , y ≥ ( 1 - x ) 2 , y ≤ 2 x ( 1 - x ) . Then 540 A is equal to

Step-by-step solution

Given, A be the area of the region ( x , y ) : y ≥ x 2 , y ≥ ( 1 - x ) 2 , y ≤ 2 x ( 1 - x ) Now solving y = x 2   &   y = 2 x 1 - x we get, x = 0 ,   2 3 And solving y = 1 - x 2   &   y = 2 x 1 - x we get, ⇒ 1 + x 2 - 2 x = 2 x - 2 x 2 ⇒ 3 x 2 - 4 x + 1 = 0 ⇒ x = 1 ,   1 3 Now on plotting the diagram of the above region we get, Now from the above diagram area of the shaded region will be, A = ∫ 1 3 2 3 2 x - 2 x 2 d x - ∫ 1 3 1 2