The area enclosed between the curves y = ax 2 and x = ay 2 a > 0 is 1 sq unit. If the value of a is 3 3 λ , then the value of λ is

Step-by-step solution

As from the figure, area enclosed between the curves is O A B C O . Thus, the points of intersection of y = ax 2 and x = ay 2 , eliminating y , we get x = a ( ax 2 ) 2 ⇒ x − a 3 x 4 = 0 ⇒ x ( 1 − a 3 x 3 ) = 6 ⇒ x = 0  and  x = 1 a ∴ Points of intersection are ( 0 ,   0 ) and 1 a , 1 a . Thus, required area O A B C O = Area of curve O C B D O - area of curve O A B D O ⇒     ∫ 0 1 / a x a - ax 2 dx = 1 (given) ⇒   1 a · ·