Answer
$$5\sqrt 2 $$
Work Step by Step
$$\eqalign{
& \int_{ - 4}^1 {\sqrt 2 } dx \cr
& {\text{use the constant multiple rule }}\int k f\left( x \right)dx = k\int {f\left( x \right)dx} \cr
& = \sqrt 2 \int_{ - 4}^1 {dx} \cr
& {\text{integrate by using }}\int {dx} = x + C.{\text{ then}} \cr
& = \sqrt 2 \left[ x \right]_{ - 4}^1 \cr
& {\text{use fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 388}}} \right) \cr
& = \sqrt 2 \left[ {1 - \left( { - 4} \right)} \right] \cr
& {\text{simplifying}} \cr
& = \sqrt 2 \left( 5 \right) \cr
& = 5\sqrt 2 \cr} $$
