AP EAMCET · Maths · Definite Integration
\(\int_9^x \frac{f(y)}{y^2} d y=2 \sqrt{x}-6 \Rightarrow f(x)=\)
- A \(\sqrt{x}\)
- B \(x \sqrt{x}\)
- C \(x^2 \sqrt{x}\)
- D \(x+\sqrt{x}\)
Answer & Solution
Correct Answer
(B) \(x \sqrt{x}\)
Step-by-step Solution
Detailed explanation
Given, \(\int_9^x \frac{f(y)}{y^2} d y=2 \sqrt{x}-6\) Differentiating both sides using Leibnitz rule, \(\frac{f(x)}{x^2}=\frac{2}{2 \sqrt{x}}\) \(\Rightarrow f(x)=\frac{x^2}{\sqrt{x}}=x \sqrt{x}\)
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