Introductory Mathematics for Engineering Applications

Integrals in Engineering

CHAPTER 9

This chapter will discuss what integration is and why engineers need to know it. It is important to point out that the objective of this chapter is not to teach techniques of integration, as discussed in a typical calculus course. Instead, the objective of this chapter is to expose students to the importance of integration in engineering and to illustrate its application to the problems covered in core engineering courses such as physics, statics, dynamics, and electric circuits.

9.1 INTRODUCTION: THE ASPHALT PROBLEM

An engineering co-op had to hire an asphalt contractor to widen the truck entrance to the corporate headquarters, as shown in Fig. 9.1. The asphalt extends 50 ft in the x- and y-directions and has a radius of 50 ft. Thus, the required asphalt is the area under the circular curve is given by

Figure 9.1 Driveway of corporate headquarters.

The asphalt company charges by the square foot and provides an estimate based on “eyeballing” the required area for new asphalt. The co-op asks a young engineer to estimate the area to make sure that the quote is fair. The young engineer proposes to estimate the area as a series of n inscribed rectangles as shown in Fig. 9.2. The area A is given by

where is the width of each rectangle and ...