Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 - x) for all x (0, 2), f(0) = 1 and f(2) = e². Then the value of ∫₀² f(x) dx is:

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 24 Feb, Evening shift · Q3393

JEE Main 202124 Feb, Evening shiftMathematicsEasyIntegral Calculus369× since 2002

Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2

-

x) for all x

\in

(0, 2), f(0) = 1 and f(2) = e². Then the value of

\int\limits_0^2 {f(x)} dx

is :