1.Let f:[1,∞)→Rf : [1, \infty) \to \mathbb{R}f:[1,∞)→R be a differentiable function such that f(1)=13f(1) = \frac{1}{3}f(1)=31 and 3∫1xf(t) dt=xf(x)−x333\int_1^x f(t)\,dt = x f(x) - \frac{x^3}{3}3∫1xf(t)dt=xf(x)−3x3, x∈[1,∞)x\in[1,\infty)x∈[1,∞). Then the value of f(e)f(e)f(e) isa.e2+43\frac{e^2 + 4}{3}3e2+4b.loge4+e3\frac{\log_e 4 + e}{3}3loge4+ec.4e23\frac{4e^2}{3}34e2d.e2−43\frac{e^2 - 4}{3}3e2−4Login to continueOnly logged in users canattempt or see the solution.
