Answer
\[ = 1\]
Work Step by Step
\[\begin{gathered}
\int_0^3 {\frac{x}{{\sqrt {25 - {x^2}} }}\,\,dx} \hfill \\
\hfill \\
rewrite\,\, \hfill \\
\hfill \\
= \frac{1}{2}\int_0^3 {\,{{\left( {25 - {x^2}} \right)}^{ - \frac{1}{2}}}\,\left( { - 2x} \right)dx} \hfill \\
\hfill \\
integrate \hfill \\
\hfill \\
= - \frac{1}{2}\,\,\left[ {\frac{{\,\left( {25 - {x^2}} \right)}}{{\frac{1}{2}}}} \right]_0^3 \hfill \\
\hfill \\
= - \,\,\left[ {\sqrt {25 - {x^2}} } \right]_0^3 \hfill \\
\hfill \\
Fundamental\,\,theorem \hfill \\
\hfill \\
= - \sqrt {25 - \,{{\left( 3 \right)}^2}} + \sqrt {25 - {0^2}} \hfill \\
\hfill \\
Simplify \hfill \\
\hfill \\
= - 4 + 5 \hfill \\
\hfill \\
= 1 \hfill \\
\hfill \\
\end{gathered} \]
