Question

Let f:[1,∞) $\rightarrow$ R be a differentiable function such that f(1) = $\frac{1}{3}$ and 3$\int_{1}^{x}$f(t)dt=xf(x)-$\frac{x^3}{3}$,x∈[1,∞). Let e denote the base of the natural logarithm. Then the value of f(e) is

• A. e2+$\frac{4}{3}$
• B. loge4+$\frac{e}{3}$
• C. $\frac{4e^2}{3}$
• D. e2-$^{\frac{4}{3}}$

Answer 1

Answer: (C)

$\frac{4e^2}{3}$

Answer 2

The correct option is (C) : $\frac{4e^2}{3}$