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