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`

Options

A. `(1)/(sqrt3)`
B. `1/2`
C. 1
D. `1/3`

Answer

A

Explanation

We have,
`underset(0)overset(1//a)(int)(y_(2)-y_(1))dx=1`

`impliesunderset(0)overset(1//a)(int){sqrt((x)/(a))-ax^(2)}dx=1`
`implies[(2)/(3sqrta)lamda^(3//2)-(a)/(3)x^(3)]_(0)^(1//a)=1implies(2)/(3sqrta)xx(1)/(a^(3//2))-q/3xx(1)/(a^(3))=1`