Question

COLLEGE MATH!!! PLEASE HELP IF YOU KNOW!!!

Answer 1

`-(3)/(2)` +
`\ln \left(3\right)`

Explanation:

`\int _(-2)^3\:g\left(t\right)dt` =
`\int _(-2)^1\:g\left(t\right)dt` +
`\int _(1)^3\:g\left(t\right)dt` =
`\int _(-2)^1\:\left(t\right)dt` +
`\int _(1)^3\:(1)/(t) dt` =
`\left[(t^(1+1))/(1+1)\right]^1_(-2)` +
`\left[\ln \left|t\right|\right]^3_1`

=
`\left[(t^2)/(2)\right]^1_(-2)` +
`\ln \left(3\right)` =
`-(3)/(2)` +
`\ln \left(3\right)`