The area of the region given by x , y : x y ≤ 8 , 1 ≤ y ≤ x 2 is :

Step-by-step solution

Given, x y ≤ 8   &   1 ≤ y ≤ x 2 On solving above curve we get intersecting point as 2 , 4 Now on plotting the diagram of the given curves we get, Required area A = ∫ 1 2 x 2 - 1 d x + ∫ 2 8 8 x - 1 d x ⇒ A = ∫ 1 2 x 2 d x + ∫ 2 8 8 x d x - ∫ 1 8 d x ⇒ A = x 3 3 1 2 + 8 ln x 2 8 - x 1 8 ⇒ A = 8 ln 4 - 14 3 ⇒ A = 16 ln 2 - 14 3 sq. units