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Home Integral Numerical Integration Examples Example 1
 
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Example 1

Approximate the definite integral

04_integration-446.gif

Use the trapezoidal approximation with Δx = 1/5. We first make a table of values of04_integration-447.gif. The graph is drawn in Figure 4.6.2.

04_integration-448.gif

Figure 4.6.2

x

04_integration-450.gif

04_integration-451.gif
to four places

term in trapezoidal
approximation

x0 = 0

1

1.0000

0.5000 = ½f(x0)

x1= 1/5

√1.04

1.0198

1.0198 = f(xl)

x2 = 2/5

√.1.16

1.0770

1.0770 = f (x2)

x3=3/5

√1.36

1.1662

1.1662 =f(x3)

x4 = 4/5

√1 .64

1.2806

1.2806 = f (x4)

x5 = 1

√2

1.4142

0.7071 = ½f(x5)

5.7507 = total

Thus, ½f(x0) + f(x1 + f(x2) + f(x3)+f(x4) + x2f(xs) = 5.7507. Since Δx = 1/5, the trapezoidal approximation is

(5.7507)·(1/5)= 1.1501,

04_integration-449.gif
Home Integral Numerical Integration Examples Example 1

Last Update: 2010-11-26