Definite-Integration Question 531
Question: If $ \int_{{}}^{{}}{f(x),dx}=x{e^{-\log |x|}}+f(x), $ then $ f(x) $ is
[MP PET 1997]
Options:
A) 1
B) 0
C) $ ce^{x} $
D) $ \log x $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_{{}}^{{}}{f(x)dx=x{e^{\log | \frac{1}{x} |}}+f(x)\Rightarrow \int_{{}}^{{}}{f(x)dx=\frac{x}{|x|}+f(x)}} $ On differentiating both sides , we get $ f(x)=0+f’(x) $ We know $ \frac{d}{dx}(e^{x})=e^{x},\therefore f(x)=ce^{x} $ .
BETA
