Closed integral confusion

[KrabLord]

I am confused as to why this problem has the following answer. I do not see how taking the integral from t=0 till t=1 satisfies a closed path. However, per green's theorem (the subject of the chapter from which I take this question), I can see that the answer is -1/2. I just do not understand how the integral is a closed path, and I want help seeing how the answer given by the textbook is appropriate.



Answer:

 

[LCKurtz]

You are correct, it isn't a closed path. It is just along the line [MATH]x+y=1[/MATH]. They are probably hoping you will observe that along the y axis, dx = 0 and along the x axis, y = 0, so those two sides contribute nothing. Good for you understanding their explanation is incomplete.

 

[KrabLord]

You are correct, it isn't a closed path. It is just along the line [MATH]x+y=1[/MATH]. They are probably hoping you will observe that along the y axis, dx = 0 and along the x axis, y = 0, so those two sides contribute nothing. Good for you understanding their explanation is incomplete.

Thank you, that is very helpful!