Q117 / 160 · AP EAMCET 2022 (08 Jul Shift 2) · Mathematics

$\int_9^x \frac{f(y)}{y^2} d y=2 \sqrt{x}-6 \Rightarrow f(x)=$

  • A
    $\sqrt{x}$
  • Correct answer
    B
    $x \sqrt{x}$
  • C
    $x^2 \sqrt{x}$
  • D
    $x+\sqrt{x}$

Solution

Given, $\int_9^x \frac{f(y)}{y^2} d y=2 \sqrt{x}-6$ Differentiating both sides using Leibnitz rule, $\frac{f(x)}{x^2}=\frac{2}{2 \sqrt{x}}$ $\Rightarrow f(x)=\frac{x^2}{\sqrt{x}}=x \sqrt{x}$

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

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