Section 16.3

Line Integrals (dx, dy)

Breaking motion into horizontal and vertical components.

Introduction

Instead of arc length , sometimes we only care about how much the field pushes in the x-direction () or y-direction ().

The common notation is: .

Given , replace differentials with time derivatives:

Evaluate where C is from (0,0) to (1,1).

1. Parameterize:

Let for .

2. Substitute:

3. Solve:

Evaluate along line from (-5,-3) to (0,2).

1. Parameterize:

. Range .

2. Substitute:

3. Solve:

Evaluate around the unit circle counter-clockwise.

1. Parameterize:

2. Calculate:

Note: This integral calculates 2x Area of Circle!