Example 3: Piecwise Smooth Curve

EXAMPLE 3

Find the line integral

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,

Figure 13.2.10