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. `root(3)(log_(e)(3y-2))`
C. `root(3)(log_(e)(2-3y))`
D. none of these

Answer

b

Explanation

We have , `y=intx^(2)e^(x^(3))dx=(1)/(3)inte^(x^(3))d(x^(3))=(1)/(3)e^(x^(3))+C`.
It passes throught ( 0 , 1) Therefore ,
`1=(1)/(3)+CrArrC=(2)/(3)`
`thereforey=(1)/(3)e^(x^(3))+(2)/(3)`
`rArr3y=e^(x^(3))+2`
` rArr e^(x^(3))=3y=2rArrx^(3)-log_(e)(3y-2)rarrc=root(3)(log_(e)(3y-2))`