AP EAMCET · Maths · Indefinite Integration
77. If \(5 f(x)+3 f\left(\frac{1}{x}\right)=2-\frac{1}{x}, x \neq 0\), then \(\int_1^2 f\left(\frac{1}{x}\right) d x=\)
- A \(\frac{6 \log 2-7}{32}\)
- B \(\frac{6 \log 2-17}{32}\)
- C \(\frac{6 \log 2-1}{32}\)
- D \(\frac{6 \log 2-7}{16}\)
Answer & Solution
Correct Answer
(A) \(\frac{6 \log 2-7}{32}\)
Step-by-step Solution
Detailed explanation
\(5 f(x)+3 f\left(\frac{1}{x}\right)=2-\frac{1}{x}\) ...(i) Put \(x=\frac{1}{x}\) in above equation: \(5 f\left(\frac{1}{x}\right)+3 f(x)=2-x\) ...(ii) Equation (ii) \(\times 5-\) (i) \(\times 3\) :…
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