JEE Main 2026 · 2 Apr · Shift 1, Mathematics question 19

Split at the integers. $[x]!=1,1,2$ on $[0,1)$, $[1,2)$, $[2,3)$:
$$\int_0^2(e^x+e^{-x})dx+\frac12\int_2^3(e^x+e^{-x})dx=\left(e^2-e^{-2}\right)+\frac12\left(e^3-e^2+e^{-2}-e^{-3}\right).$$

Simplify. $=\dfrac12\left(e^2+e^3-\dfrac1{e^2}-\dfrac1{e^3}\right)$.

(B)