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).
Solution :
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)
i.e.
or,
So, along (x is an independent variable)
Along (let us take x as independent variables).
on
So,
Example 2 :
Evaluate where
where curve C is a rectangle in the xy plane bounded by y = 0, x = a, y = b, x = 0.
Solution :
The curve C as shown in figure consists of four pieces of smooth curves
On
On
On
On