Chapter 4.6, Problem 42E

Electrical energy use. The rate at which electrical energy is used by the Ortiz family, in kilowatt-hours (kW-h) per day, is given by

$K\left(t\right)=10t{e}^{-t}$,

where t is time, in hours. That is, t in the interval $\left[0,24\right]$.

$-10T{e}^{-T}-{10}^{-T}+10$

a. How many kilowatt-hours does the family use in the first T house of a day $\left(t=0\text{ to }t=T\right)$?

b. How many kilowatt-hours does the family use in the first 4 house of a day?