The area bounded between the curves y=a x^2 and x= a y^2( a 0) is 1 sq. units, then the value of a is

Step-by-step solution

The two curves intersect at O(0,0) and P ( 1 a , 1 a ) . According to the given condition, aligned & ₀^ 1 2 ( x a - a x^2 ) d x=1 & [ 2 3 a x^ 3 / 2 - a x^3 3 ]₀^ 1 / a =1 & 2 3 a 1 a ^ 3 / 2 - a 3 1 a ^3 =1 & 2 3 a ^2 - 1 3 a ^2 =1 1 3 a ^2 =1 & a = 1 3 [ a 0] aligned