QJEEM21Ma0a38: JEE Main 2021 Mathematics - Class 12 JEEM21Ma0a38 Solution: Let f(x) be a differentiable function defined on [0, 2] such…

Question

Verified Solution • 2025–26 Session moderate

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_{0}^{2} f (x) d x

is :

Accepted Answer

f'(x) = f'(2

-

x)

On integrating both side f(x) =

-

f(2

-

x) + c

put x = 0

f(0) + f(2) = c

\Rightarrow

c = 1 + e²

\Rightarrow

f(x) + f(2

-

x) = 1 + e² ..... (i)

I = \int_{0}^{2} f (x) d x = \int_{0}^{1} {f (x) + f (2 - x)} d x = (1 + e^{2})

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