The value of the function f(x)=1+x+ _ 1 ^ x ( ^ 2 t+2 t ) d t where f^ (x) vanishes is
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
The value of the function
\(f(x)=1+x+\int_{1}^{x}\left(\ln ^{2} t+2 \ln t\right) d t\) where \(f^{\prime}(x)\) vanishes is
\(f(x)=1+x+\int_{1}^{x}\left(\ln ^{2} t+2 \ln t\right) d t\) where \(f^{\prime}(x)\) vanishes is
- \(e^{-1}\)
- \(0\)
- \(2 e^{-1}\)
- \(1+2 e^{-1}\)
Answer
(D) 1+2 e^ -1
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