Question

\[\int\limits_0^1 e^\left\{ x \right\} dx .\]

Answer 1

\[\text{We have}, \]
\[I = \int_0^1 e^\left\{ x \right\} d x\]
\[\text{We know that}, \]
\[\left\{ x \right\} = x\text{, when }0 < x < 1\]
\[ \therefore I = \int_0^1 e^x d x\]
\[ = \left[ e^x \right]_0^1 \]
\[ = e^1 - e^0 \]
\[ = e - 1\]