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Let \([\cdot ]\) denote the greatest integer function. Then the value of \({\int }_{0}^{3}\left(\frac{{e}^{x}+{e}^{-x}}{…

Q1

Let \([\cdot ]\) denote the greatest integer function. Then the value of \({\int }_{0}^{3}\left(\frac{{e}^{x}+{e}^{-x}}{\left[|x|\right]!}\right)dx\) is:

[JEE Main 2026, 2 Apr (Shift 1)]

a

\({e}^{2}+{e}^{3}-\frac{1}{{e}^{2}}-\frac{1}{{e}^{3}}\)

b

\(\frac{1}{2}\left({e}^{2}+{e}^{3}-\frac{1}{{e}^{2}}-\frac{1}{{e}^{3}}\right)\)

c

\({e}^{2}+{e}^{3}-\frac{1}{2{e}^{2}}-\frac{1}{2{e}^{3}}\)

d

\(\frac{1}{2}\left({e}^{2}+{e}^{3}\right)-\frac{1}{{e}^{2}}-\frac{1}{{e}^{3}}\)

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