(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\oint[/tex]xydx+x^2dy

C is the rectangle with vertices (0,0),(0,1),(3,0), and (3,1)

Evaluate the integral by two methods: (a) directly and (b) using green's theorem.

2. Relevant equations

3. The attempt at a solution

Evaluating the integral directly:

c1: y=0,x=t,dx=dt,dy=o {0[tex]\leq[/tex]t[tex]\leq[/tex]3}

c2: x=3, y=t, dx=0, dy=dt {0[tex]\leq[/tex]t[tex]\leq[/tex]1}

c3: y=1, dy=0, x=t, dx=dt {0[tex]\leq[/tex]t[tex]\leq[/tex]3}

c4: x=0, dx=0, y=t, dy=dt {0[tex]\leq[/tex]t[tex]\leq[/tex]1}

So I got c1 and c4 being the integral of zero which is just zero.

Then for c2 and c3...

[tex]\int[/tex]9dt {t:0[tex]\leq[/tex]t[tex]\leq[/tex]1} +[tex]\int[/tex]tdt {t:0[tex]\leq[/tex]t[tex]\leq[/tex]3}=27/2

Then trying to use green's theorem:

[tex]\int[/tex][tex]\int[/tex]xdydx=[tex]\int[/tex]xdx=9/2

{y:0[tex]\leq[/tex]y[tex]\leq[/tex]1}

{x:0[tex]\leq[/tex]x[tex]\leq[/tex]3}

I am not sure where I messed up but I know I did because both of my answers should be the same. If someone could point me in the right direction, it would be much appreciated. Thank you for your time.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Green's Theorem and Line Integral

**Physics Forums | Science Articles, Homework Help, Discussion**