x Turn on thread page Beta
 You are Here: Home >< Maths

Green's theorem watch

1. "Evaluate the line integral

where the C is the perimeter of the triangle with the vertices (0,0), (1,0) and (1,1). Hence use double integration to verify Green's theorem."

Now from the line integral I get the answer 1/3, the double integral with both limits going from 0 to 1.

The partial differential being 2y and integrating this w.r.t y first gives y^2, hence 1.....then w.r.t x this gives x. Thus the final answer is 1.......where am I going wrong?
2. Thing about what both limits going from 0 to 1 actually represents: it represents integration over the square [0,1] x [0,1]. But you want to integrate over a triangle instead, whereby our integral limits are not so easy. Now, take our triangle, and fix x. For a fixed x, where does y range? It shouldn't be too hard to convince yourself that y ranges from 0 to x. Thus our integral becomes .
3. (Original post by Glutamic Acid)
Thing about what both limits going from 0 to 1 actually represents: it represents integration over the square [0,1] x [0,1]. But you want to integrate over a triangle instead, whereby our integral limits are not so easy. Now, take our triangle, and fix x. For a fixed x, where does y range? It shouldn't be too hard to convince yourself that y ranges from 0 to x. Thus our integral becomes .
That's amazing! is this always the case when it comes to a triangle?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 20, 2011
Today on TSR

Ask the House of Commons anything

The digital outreach team is online until 4pm!

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants