AP EAMCET · Maths · Indefinite Integration
If the graph of the anti derivative \(g(x)\) of \(f(x)=\log (\log\) \(x)+(\log x)^{-2}\) passes through \((e, 2023-e)\) and the term independent of \(x\) in \(g(x)\) is \(k\), then the sum of all the digits of \(\mathrm{k}\) is
- A 5
- B 6
- C 7
- D 8
Answer & Solution
Correct Answer
(C) 7
Step-by-step Solution
Detailed explanation
Given : \(f(x)=\log (\log x)+(\log x)^{-2}\) Anti-derivative of \(f(x)=\int\left(\log (\log x)+(\log x)^{-2}\right) d x\) ...(i) Let \(t=\log x \Rightarrow x=e^t\) \(\Rightarrow d x=e^t d t\) Using above values in eqn. (i), we get : Anti-derivative of…
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