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

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

A

f(x) + ex .f(x)

B

f(x) – ex . f(x)

C

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

D

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

Answer

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

Explanation

Solution

Here ∫ex\int_{}^{}e^{x} (f(x) – f '(x)) dx = f(x)

& (f(x) – f '(x)) dx = ex.f(x)

Add ̃ 2 ∫.ex\int_{}^{}{.e^{x}}. f(x)dx = f(x) + ex f(x)