If the area of the region bounded by the curves y 2 - 2 y = - x and x + y = 0 is A , then 8 A =

Step-by-step solution

Given, Equations of curve y 2 - 2 y = - x and x + y = 0 Now solving above equations we get, x = 0 , - 3 Now plotting the area we get, Now from above diagram required area will be A = ∫ 0 3 2 y - y 2 + y d y ⇒ A = ∫ 0 3 3 y - y 2 d y ⇒ A = 3 y 2 2 - y 3 3 0 3 ⇒ A = 27 2 - 27 3 ⇒ A = 27 6 = 9 2 sq. units So, A = 9 2 ⇒ 8 A = 9 × 4 = 36 .