Answer
$2$
Work Step by Step
Solve $\int_{\ln 4}^{\ln 9} e^{x/2} dx$
Let us $p= \dfrac{x}{2}$ and $dp=\dfrac{1}{2}dx$
This implies $\int_{\ln 4}^{\ln 9} e^{x/2} dx= 2\int_{\ln 4}^{\ln 9} e^p dp$
$= 2[e^p]_{\ln 4}^{\ln 9}+c$
$= 2[e^{ \frac{x}{2}}]_{\ln 4}^{\ln 9} +c$
$= 2[e^{ \frac{\ln 9}{2}}-e^{ \frac{\ln 4}{2}}]+c$
Also, $=2[3-2]$
Hence, $\int_{\ln 4}^{\ln 9} e^{x/2} dx=2$
