Question

Let the equation of a curve passing through point (0, 1) be given by y = $\int_{}^{}{x^{2}.e^{x^{3}}}$ dx. If the equation of the curve is written in the form x = f(y) then f(y) is –

• A. $\sqrt{\log_{e}(3y–2)}$
• B. $\sqrt[3]{\log_{e}(3y–2)}$
• C. $\sqrt[3]{\log(2–3y)}$
• D. None of these

Answer 1

Answer: (B)

$\sqrt[3]{\log_{e}(3y–2)}$

Answer 2

Sol. y = $\int_{}^{}{\frac{1}{3}e^{x^{3}}}$.d(x³) = $\frac{1}{3}$ $e^{x^{3}}$ + c

Point to (0, 1) Ž 1 = $\frac{1}{3}$ e⁰ + c Ž c = 2/3

Ž hence y = $\frac{e^{x^{3}}}{3}$ + $\frac{2}{3}$ Ž $e^{x^{3}}$ = 3y – 2

Ž x = $\sqrt[3]{\log_{e}(3y–2)}$ = f(y)