Let f: R → R be defined as f(x) = e⁻ˣsinx. If F: [0, 1] → R is a differentiable function with that F(x) = ∫₀ˣ f(t)dt, then the value of ∫₀¹ (F'(x) + f(x))eˣdx lies in the interval

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 17 Mar, Evening shift · Q3311

JEE Main 202117 Mar, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let f : R

\to

R be defined as f(x) = e^

-

xsinx. If F : [0, 1]

\to

R is a differentiable function with that F(x) =

\int_0^x {f(t)dt}

, then the value of

\int_0^1 {(F'(x) + f(x)){e^x}dx}

lies in the interval