Answer
\[ = 20\]
Work Step by Step
\[\begin{gathered}
\int_0^2 {\,{{\left( {x + 1} \right)}^3}dx} \hfill \\
\hfill \\
integrate \hfill \\
\hfill \\
= \,\,\left[ {\frac{{\,{{\left( {x + 1} \right)}^4}}}{4}} \right]_0^2 \hfill \\
\hfill \\
Fundamental\,\,theorem \hfill \\
\hfill \\
= \frac{{\,{{\left( {2 + 1} \right)}^4}}}{4} - \frac{{\,{{\left( {0 + 1} \right)}^4}}}{4} \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
= \frac{{81}}{4} - \frac{1}{4} = \frac{{80}}{4} \hfill \\
\hfill \\
= 20 \hfill \\
\end{gathered} \]
