Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

622 Chapter 18 Mathematics in Engineering

Step 3: We make use of the relationship between the fluid pressure and depth of the fluid, that

is,prgy.

Step 4: We simplify by assuming a constant fluid density and constantg.

Step 5: We substitute fordAwdy, wherewis the width of the dam.

Step 6: The solution. We will discuss the integration rules later.

We could come up with many more examples to emphasize the role of integrals in engi-

neering applications.

During the next few years, as you take your calculus classes, you will learn many new con-

cepts and rules dealing with integral calculus. Make sure you take the time to understand these

concepts and rules. Some of these integral concepts and rules are summarized in Table 18.7.

Examples that demonstrate how to apply some of these rules follow. As you study the examples,

keep in mind again that our intent is to familiarize you with these rules, not to provide a detailed

coverage.

Example 18.15 Evaluate

We use rules 2 and 6 from Table 18.7 to solve this problem, as shown.

x

3

 10 x

2

C

 3 c

1

2  1

x

3

d 20 c

1

1  1

x

2

dC

(^)  13 x
2
 20 x 2 dx  3 x
2
dx  20 x dx (^3) x
2
dx (^20) x dx
^13 x
2
 20 x 2 dx.
y dF dA
P  gy
H
■Figure 18.21 The forces due to pressure acting on a vertical surface.
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