Question

Let f: [1,∞) → [2,∞) be a differentiable function such that f(1) = 2, if 6 ∫f(t) dt for t ∈ [1,x] = 3 xf(x) – x³ for all x ≥ 1, the value of f(2) is ...

Answer 1

Given,

which is a linear differential equation.

y/x = – (1/x) + c 

when x = 1, y = 2, then c = 3 

Thus, the equation of the curve is 

y/x = – (1/x) + 3 

Now, when x = 2, then 

y = –1 + 3x = –1 + 6 = 5