TS EAMCET · Maths · Definite Integration
If \(f(x)=\frac{1}{x^2} \int_3^x\left(2 t-3 f^{\prime}(t)\right) d t\), then \(f^{\prime}(3)\) is equal to
- A \(\frac{-1}{2}\)
- B \(\frac{-1}{3}\)
- C \(\frac{1}{2}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Given that, \[ f(x)=\frac{1}{x^2} \int_3^x\left(2 t-3 f^{\prime}(t)\right) d t \] On differentiating both sides w.r.t. \(x\), we get…
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