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Example 3: Piecwise Smooth Curve

EXAMPLE 3

Find the line integral

13_vector_calculus-83.gif

where C is the rectangular curve from (2, 5) to (4, 5) to (4, 6).

We see in Figure 13.2.10 that C is a piecewise smooth curve made up of a horizontal piece

C1:2 ≤ x ≤ 4, y = 5

and a vertical piece

C2:x = 4, 5 ≤ y ≤ 6.

The line integral is the sum of two partial integrals,

13_vector_calculus-84.gif

Figure 13.2.10

13_vector_calculus-85.gif


Last Update: 2006-11-20