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MathsJEE Main 2 Apr 2026, Shift 1·Q19·MCQ·Easy–moderate

Definite Integration · Integral with greatest integer function

Let [⋅][\cdot] denote the greatest integer function. Then the value of ∫03(ex+e−x[x]!)dx\displaystyle\int_0^3\left(\frac{e^x + e^{-x}}{[x]!}\right)dx is:
  1. (1)e2+e3−1e2−1e3e^2 + e^3 - \dfrac{1}{e^2} - \dfrac{1}{e^3}
  2. (2)12(e2+e3−1e2−1e3)\dfrac12\left(e^2 + e^3 - \dfrac{1}{e^2} - \dfrac{1}{e^3}\right)
  3. (3)e2+e3−12e2−12e3e^2 + e^3 - \dfrac{1}{2e^2} - \dfrac{1}{2e^3}
  4. (4)12(e2+e3)−1e2−1e3\dfrac12(e^2 + e^3) - \dfrac{1}{e^2} - \dfrac{1}{e^3}

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