1. Section 18.2 Computing Line Integrals over Parameterized Curves

2. Last section we began to examine line integrals
Now we need to figure out how to evaluate them
Main problem: Evaluate the following
where C is the oriented curve parameterized by
In 2 space
In 3 space

3. If C is piecewise smooth and is a continuous vector field we have

4. In 3 space

5. and C is the right hand side of the unit circle
Example 1
and C is the right hand side of the unit circle
So we will need the parameterization of C
Example 2
and C is the triangle joining (1,0), (0,1) and (-1,0)
In this case we will need to find parametric equations for each curve
Let’s look at calculating line integrals with Maple