Chapter 5 - Integration - 5.3 Fundamental Theorem of Calculus - 5.3 Exercises - Page 376: 86

$$\frac{1}{2}$$

$$\eqalign{ & \frac{1}{2}\int_0^{\ln 2} {{e^x}} dx \cr & \frac{d}{{dx}}\left[ {{e^x}} \right] = {e^x},{\text{ then}} \cr & \frac{1}{2}\int_0^{\ln 2} {{e^x}} dx = \frac{1}{2}\left. {\left( {{e^x}} \right)} \right|_0^{\ln 2} \cr & {\text{using the fundamental theorem}} \cr & = \frac{1}{2}\left( {{e^{\ln 2}} - {e^0}} \right) \cr & {\text{simplify}} \cr & = \frac{1}{2}\left( {2 - 1} \right) \cr & = \frac{1}{2} \cr} $$