Answer
$$1$$
Work Step by Step
$$\eqalign{
& \int_{\ln 2}^{\ln 3} {{e^x}} dx \cr
& {\text{use the formula }}\int_a^b {{e^{kx}}} dx = \left( {\frac{{{e^{kx}}}}{k}} \right)_a^b \cr
& \int_{\ln 2}^{\ln 3} {{e^x}} dx = \left( {{e^x}} \right)_{\ln 2}^{\ln 3} \cr
& {\text{use fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 281}}} \right) \cr
& \int_{\ln 2}^{\ln 3} {{e^x}} dx = {e^{\ln 3}} - {e^{\ln 2}} \cr
& {\text{simplifying}} \cr
& \int_{\ln 2}^{\ln 3} {{e^x}} dx = 3 - 2 \cr
& \int_{\ln 2}^{\ln 3} {{e^x}} dx = 1 \cr} $$
