Answer
\[g(t)=2\sin ^{-1}t+5-π\]
Work Step by Step
\[g'(t)=\frac{2}{\sqrt{1-t^2}}\]
\[\frac{dg}{dt}=\frac{2}{\sqrt{1-t^2}}\]
Separating variables,
\[dg=\frac{2}{\sqrt{1-t^2}}dt\]
Integrating
\[\int dg=\int \frac{2}{\sqrt{1-t^2}}dt\]
\[g(t)=2\sin ^{-1}t+C\]
Where $C$ is constant of integration
Using given data $g(1)=5$
\[g(1)=2\sin ^{-1}1+C\]
\[5=2\cdot (\frac{π}{2})+C\]
\[C=5-π\]
Hence , \[g(t)=2\sin ^{-1}t+5-π\]
