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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) isA. `sqrt(log_(e)(3y-2))`B. `(log_(e)(3y-2))^(1//3)`C. `(log_(e)(2-3y))^(1//3)`D. None of these |
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Answer» Correct Answer - B `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)` |
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