Answer
$$12$$
Work Step by Step
$$\eqalign{
& \int_{ - 2}^2 {\left( {4z + 3} \right)dz} \cr
& {\text{integrate by using }}\int {{t^n}} dt = \frac{{{t^{n + 1}}}}{{n + 1}} + C{\text{ and }}\int {dt} = t + C \cr
& = \left[ {4\left( {\frac{{{z^{1 + 1}}}}{{1 + 1}}} \right) + 3\left( z \right)} \right]_{ - 2}^2 \cr
& = \left[ {2{z^2} + 3z} \right]_{ - 2}^2 \cr
& {\text{use fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 388}}} \right) \cr
& = \left( {2{{\left( 2 \right)}^2} + 3\left( 2 \right)} \right) - \left( {2{{\left( { - 2} \right)}^2} + 3\left( { - 2} \right)} \right) \cr
& {\text{simplifying}} \cr
& = \left( {8 + 6} \right) - \left( {8 - 6} \right) \cr
& = 14 - 2 \cr
& = 12 \cr} $$
