If f: R R is a function satisfying the following : (i) f (– x ) = – f ( x ) (ii) f ( x +…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If \(f: \mathrm{R} \rightarrow \mathrm{R}\) is a function satisfying the following :
(i) f (–x) = –f (x)
(ii) f (x + 1) = f (x) + 1
(iii) \(f\left(\frac{1}{x}\right)=\frac{f(x)}{x^{2}} \forall x \neq 0\)
then \(\int e^{x} f(x) d x\) is equal to
(i) f (–x) = –f (x)
(ii) f (x + 1) = f (x) + 1
(iii) \(f\left(\frac{1}{x}\right)=\frac{f(x)}{x^{2}} \forall x \neq 0\)
then \(\int e^{x} f(x) d x\) is equal to
- ex (x – 1) + c
- ex log x + c
- \(\frac{e^{x}}{x}+c\)
- \(\frac{e^{x}}{x+1}+c\)
Answer
(A) e x ( x – 1) + c
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