JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

f: \mathbb{R} \rightarrow \mathbb{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

View answer and explanation

Correct option: A

e^x(x-1)+c

The correct answer is A (

e^x(x-1)+c

) because after determining that

f(x) = x

, the integral

\int e^x f(x) dx

simplifies to

\int xe^x dx

, which can be solved using integration by parts.

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{C}

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