Calculate line integral , where c is triangle with vertices at points (0,0), (1,0) and (1,2).

How can I find r(t) ?

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- April 25th 2009, 11:30 AMApprentice123Compute the line integral
Calculate line integral , where c is triangle with vertices at points (0,0), (1,0) and (1,2).

How can I find r(t) ? - April 25th 2009, 11:51 AMJhevon
you have to state what direction you are going in. is it from (0,0) to (1,0) to (1,2)??

you will have to do three separate integrals, one for each side of the triangle. for each, your r(t) will be the vector function for the line.

Here is how to proceed:

Assuming we are going from (0,0) to (1,0) to (1,2), call the line connecting (0,0) to (1,0) , the line connecting (1,0) and (1,2) and the line connecting (1,2) back to (0,0) .

Then we have .

lets concentrate on .

for , we have the line , with x ranging from 0 to 1. thus, we can parametrize the line by:

, , for

and so, , , and our integral for becomes:

now do the same for and .

(note, there is no need to introduce a here. we could have parametrized our line by , for ) - April 25th 2009, 03:36 PMApprentice123Line integral
thank you