Chapter 8, Problem 5RE

To determine

To determine the number of kilowatt-hours of electrical energy consumed by a company in a day.

Answer to Problem 5RE

  $14400$ kilowatts of electrical energy is consumed by a company in a day.

Explanation of Solution

Given:

The electrical power consumption (measured in kilowatts) at a factory $t$ hours after midnight during a typical day is modeled by $E\left(t\right)=300\left(2-\cos \left(\pi t/12\right)\right)$ .

Calculation:

Since, the electrical power consumption is given by

  $E\left(t\right)=300\left(2-\cos \left(\pi t/12\right)\right)$

The number of kilowatt-hours of electrical energy consumed by a company in a day is

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{24}{\int }}E\left(t\right)dt}={\displaystyle \underset{0}{\overset{24}{\int }}300\left(2-\cos \left(\pi t/12\right)\right)}dt={\left|600t-\frac{\sin \left(\pi t/12\right)}{\pi /12}\right|}_0^{24}\\ =\left(600\times 24-\frac{\sin \left(\pi \times 24/12\right)}{\pi /12}\right)-\left(600\times 0-\frac{\sin \left(\pi \times 0/12\right)}{\pi /12}\right)=14400\end{array}$

Therefore, $14400$ kilowatts of electrical energy is consumed by a company in a day.