Answer
\[5\left( {{e^2} - 1} \right)\]
Work Step by Step
\[\begin{gathered}
\int_0^1 {10{e^{2x}}} dx \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
10\int_0^1 {{e^{2x}}} dx \hfill \\
\hfill \\
{\text{integrating}} \hfill \\
\hfill \\
10\left( {\frac{1}{2}} \right)\left[ {{e^{2x}}} \right]_0^1 \hfill \\
\hfill \\
5\left[ {{e^{2x}}} \right]_0^1 \hfill \\
\hfill \\
{\text{Use the fundamental theorem of calculus}} \hfill \\
\hfill \\
5\left[ {{e^{2\left( 1 \right)}} - {e^{2\left( 0 \right)}}} \right] \hfill \\
\hfill \\
{\text{Simplify}} \hfill \\
\hfill \\
5\left( {{e^2} - 1} \right) \hfill \\
\end{gathered} \]
