Parametric equation, is there such thing as minus and plus?

[flyingpig]

Homework Statement

Evaluate the line integral directly

[tex]\oint_C xy^2 dx + x^3 dy[/tex]

C is the rectangle with vertices (0,0), (2,0), (2,3), (0,3)

The Attempt at a Solution

I am having problems with parametrizing the line y = 3

I did

[tex] x = 2t, y = 3, t\in [0,2][/tex]

Solutions

[PLAIN]http://img6.imageshack.us/img6/4743/unledtp.jpg

I am a little confused, the book's parametrization looked as if C₃ is a vector function.

 

[Mark44]

C₁, C₂, etc. are directed line segments.

 

[flyingpig]

What does that mean? directed?

 

[SteamKing]

"Directed" means that if you look at the diagram of the region closely, you will see that the line integral is intended to be evaluated when the perimeter of the rectangle is traversed in a counterclockwise direction, relative to the origin. This means that some of the limits of integration require adjustment in your calculations.