Let $f: \mathbf{R} \rightarrow(0, \infty)$ be a continuous decreasing function. Suppose $f(0), f(1), \ldots, f(10)$ are in a geometric progression with common ratio $\frac{1}{5}$. In which of the following intervals does the value of $\int_0^{10} f(x) d x$ lie?

• A

  $(4 f(0), 6 f(0))$
• B

  $(8 f(0), 10 f(0))$
• C

  $(12 f(0), 14 f(0))$
• Correct answer
  D

  $(0,2 f(0))$

Hence, the correct answer is option: 'D'.