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Question: Let \(\int_{}^{}{e^{x}\{ f(x)–f'(x)\} dx}\) = f(x) then \(\int_{}^{}{e^{x}f(x)}\)dx is...

Let ∫ex{f(x)–f′(x)}dx\int_{}^{}{e^{x}\{ f(x)–f'(x)\} dx} = f(x) then ∫exf(x)\int_{}^{}{e^{x}f(x)}dx is

A

f(x) + exf(x)

B

12\frac{1}{2} (f(x) + exf(x))

C

f(x) – exf(x)

D

ex f(x)

Answer

12\frac{1}{2} (f(x) + exf(x))

Explanation

Solution

– [exf(x) – dx] = f(x)

= 12\frac { 1 } { 2 }(exf(x) + f(x)).