Question:medium
Let
\[ f(x) + 2f\left(\frac{1}{x}\right) = \frac{1}{x} - 5 \]
Then
\[ \int_{1}^{2} 3f(x)\,dx \]
equals ______.
Let
\[ f(x) + 2f\left(\frac{1}{x}\right) = \frac{1}{x} - 5 \]
Then
\[ \int_{1}^{2} 3f(x)\,dx \]
equals ______.
Show Hint
Always form a second equation using \(x \to 1/x\) when both \(f(x)\) and \(f(1/x)\) appear.
Updated On: Apr 30, 2026
- \(2 + \ln 2\)
- \(2 - \ln 2\)
- \(2\)
- \(3 \ln 2\)
- \(\ln 2\)
Show Solution
The Correct Option is B
Solution and Explanation
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