Answer:
[tex]-\frac{3}{2}[/tex] + [tex]\ln \left(3\right)[/tex]
Step-by-step explanation:
[tex]\int _{-2}^3\:g\left(t\right)dt[/tex] = [tex]\int _{-2}^1\:g\left(t\right)dt[/tex] + [tex]\int _{1}^3\:g\left(t\right)dt[/tex] = [tex]\int _{-2}^1\:\left(t\right)dt[/tex] + [tex]\int _{1}^3\:\frac{1}{t} dt[/tex] = [tex]\left[\frac{t^{1+1}}{1+1}\right]^1_{-2}[/tex] + [tex]\left[\ln \left|t\right|\right]^3_1[/tex]
= [tex]\left[\frac{t^2}{2}\right]^1_{-2}[/tex] + [tex]\ln \left(3\right)[/tex] = [tex]-\frac{3}{2}[/tex] + [tex]\ln \left(3\right)[/tex]
