JEE Mains · Maths · STD 12 - 7.2 definite integral
For \(x > 0,\) if \(f(x)=\int_{1}^{x} \frac{\log _{e} t}{(1+t)} d t,\) then \(f(e)+f\left(\frac{1}{e}\right)\) is equal to ...... .
- A \(1\)
- B \(-1\)
- C \(\frac{1}{2}\)
- D \(0\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(f( x )=\int_{1}^{ x } \frac{\log _{ e } t }{(1+ t )} d t\) \(f\left(\frac{1}{ x }\right)=\int_{ i }^{1 / x } \frac{\ell nt }{1+ t } dt ,\) let \(t =\frac{1}{ y }\) \(=+\int_{1}^{x} \frac{\ell n y}{1+y} \cdot \frac{y}{y^{2}} d y\)…
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