The set of real numbers $a \gt 0$ for which the inequality
$\frac{1}{\sqrt{a}} \int_1^a\left(\frac{3}{2} \sqrt{x}+1-\frac{1}{\sqrt{x}}\right) d x \lt 4$
is valid, lie in the interval

• Correct answer
  A

  $(0,4)$
• B

  $(0,2)$
• C

  $(2,3)$
• D

  $(1,4)$

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