JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

f

be a continuous function on

\mathbf{R}

satisfying

f(x+y)=f(x)+f(y)

for all

x, y \in \mathbf{R}

with

f(1)

=2

and

g

be a function satisfying

f(x)+g(x)=

e^x

then the value of the integral

\int\limits_{0}^1 f(x) g(x) \mathrm{d} x

View answer and explanation

Correct option: C

2 / 3

Option C (2/3) is correct because after determining

f(x) = 2x

and

g(x) = e^x - 2x

, the integral

\int_0^1 f(x)g(x) dx

evaluates to 2/3.

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