Let f: R → R be a differentiable function such that f^()(x)+f(x)=∫₀² f(t) d t. If f(0)=e⁻², then 2 f(0)-f(2) is equal to _ _ _ _ _ _.

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 1 Feb, Morning shift · Q27

JEE Main 20231 Feb, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Let

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

be a differentiable function such that

f^{\prime}(x)+f(x)=\int_\limits{0}^{2} f(t) d t

. If

f(0)=e^{-2}

, then

2 f(0)-f(2)

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2023 Integral Calculus Question with Answer (1 Feb Morning shift, Q27) | JEE Arc