If the area enclosed between the curves `y=a x^2a n dx=a y^2(a >0)` is `1` square unit, then find the value of `adot`

Explanation

Given two curves `y=a x^2`and `x=a y^2(a >0)`
from these equation we get,
`=>x=a(a x^2)^2`
`=>x=0,1/a`
`=>y=0,1/a`
`∴ `Point of intersection are `(0,0)` and `(1/a,1/a)`
Thus, required area `OABCO`= Area of curve OCBDO− area of curve `OABDO`
`=>int_0^1/a(sqrt(x/a)-ax^2)dx=1`(given)
`=>[1/a^2*x^(3/2)/(3/2)-(ax)^3/3]_0^(1/a)=1`
`=>2/(3a^2)-1/(3a^2)=1`
`=>a^2=1/3`
`=>a=1/sqrt3`