Solving an Integral with a Bent Line Path

[mit_hacker]

Homework Statement

∫_C▒〖xyds:〗

where C is the bent line from (0,0) to (1,1) and then to (1,0).

Homework Equations

The Attempt at a Solution

I split the paths into two pieces. In the first one, x=t, y=t and we integrate from 0 to 1. However, for the second part, I am unable to come up with the parameterization. Please advise on how this is done.

 

[siddharth]

I split the paths into two pieces. In the first one, x=t, y=t and we integrate from 0 to 1. However, for the second part, I am unable to come up with the parameterization. Please advise on how this is done.

Notice that in the second case, the value of x stays constant, while the value of y varies from 1 to 0. So, what parameterization suggests itself?

 

[mit_hacker]

Is it...

Is it x=1 and y=t from 0 < t < 1??

 

[siddharth]

Is it x=1 and y=t from 0 < t < 1??

Not quite. Remember you want y to go from 1 to 0, while t goes from 0 to 1. If you take y=t, then y goes from 0 to 1 as t goes from 0 to 1

 

[mit_hacker]

How about this?

Is it x=1 and y=1-t from 0 < t < 1??

 

[HallsofIvy]

Yes, that works.