Let f(x), (x≥1) be a differentiable function satisfying f(x)=(lnx)2−e∫1f(t)tdt. If the area bounded by the tangent line of y=f(x) at point (e,f(e)), the curve y=f(x) and the line x=1 is A. Then the value of [A] is , where [.] denotes the greatest integer function.

Let f(x), (x≥1) be a differentiable function satisfying f(x)=(lnx)2�

1.	Let f(x), (x≥1) be a differentiable function satisfying f(x)=(lnx)2−e∫1f(t)tdt. If the area bounded by the tangent line of y=f(x) at point (e,f(e)), the curve y=f(x) and the line x=1 is A. Then the value of [A] is , where [.] denotes the greatest integer function.
Answer» Let $f (x), (x \geq 1)$ be a differentiable function satisfying $f (x) = (ln x)^{2} - e \int 1 \frac{f (t)}{t} d t .$ If the area bounded by the tangent line of $y = f (x)$ at point $(e, f (e)),$ the curve $y = f (x)$ and the line $x = 1$ is $A$ . Then the value of $[A]$ is , where $[.]$ denotes the greatest integer function.