Example : 1
Evaluate the line integral where and C is curve in xy plane consisting of the straight lines from (0, 0) to (1, 0) and then to (3, 4).
The curve C consists of two pieces of smooth curves and .
is straight line from (0, 0) to (1, 0) ie. y = 0
is straight line from (1, 0) to (3, 4)
So, along (x is an independent variable)
Along (let us take x as independent variables).
Example 2 :
Evaluate where where curve C is a rectangle in the xy plane bounded by y = 0, x = a, y = b, x = 0.
The curve C as shown in figure consists of four pieces of smooth curves