Let the equation of a curve passing through the point (0,1) be given b `y=intx^2e^(x^3)dx`. If the equation of the curve is written in the form `x=f(y)`, then f(y) is

Options

A. `sqrt(log_(e)(3y-2))`
B. `(log_(e)(3y-2))^(1//3)`
C. `(log_(e)(2-3y))^(1//3)`
D. None of these

Answer

B

Explanation

`y=int x^(2)e^(x^(2)) dx x^(3) =t`
`x^(2) dx = 1/3 dt` ltbtgt `y=1/3 e^(x^(3)) +c`
passes through (0,1)
`1=1/3 +c rArr c= 2/3`
from (1), we have `y=1/3 e^(x^(3)) +2/3`
`rArr e^(x^(3)) =3y -2 rArr x^(3) =e n_(e)(3y-2)`
`rArr x = (en_(e)(3y -2))^(1//3)`