Answer
\[\left| {Area} \right| = \frac{{94}}{3}\]
Work Step by Step
\[\begin{gathered}
f\left( x \right) = {x^2} - 25{\text{ on }}\left[ {2,4} \right] \hfill \\
\hfill \\
Area = \int_a^b {f\left( x \right)dx} \hfill \\
\hfill \\
then \hfill \\
\hfill \\
Area = \int_2^4 {\left( {{x^2} - 25} \right)} dx \hfill \\
\hfill \\
{\text{integrate}} \hfill \\
\hfill \\
Area = \left[ {\frac{{{x^3}}}{3} - 25x} \right]_2^4 \hfill \\
\hfill \\
evaluate{\text{ the limits}} \hfill \\
\hfill \\
Area = \left[ {\frac{{{{\left( 4 \right)}^3}}}{3} - 25\left( 4 \right)} \right] - \left[ {\frac{{{{\left( 2 \right)}^3}}}{3} - 25\left( 2 \right)} \right] \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
Area = - \frac{{236}}{3} + \frac{{142}}{3} \hfill \\
\hfill \\
Area = - \frac{{94}}{3} \hfill \\
\hfill \\
\left| {Area} \right| = \frac{{94}}{3} \hfill \\
\hfill \\
\end{gathered} \]
