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**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

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