Line integral to find r(t)

Ineed, I can have. The question is again why they alerted us to have an open path while we will never have a closed path?
Seems we agree that one can have open paths even when the angle is same. The problem asks for an open path because an integral of a gradient along a closed path is always zero. You can try proving the last statement as an exercise.
 
hmm now it makes sense since \(\displaystyle C_2\) has an integral equals to one.

Thanks a lot blamocur for spending your time here to help me. Let's just hope that we meet again in a more enjoyable exercise (question).
 
It's a pleasure to help those who want to learn -- as opposed to posters who want to bypass learning :(
 
You mean some people want free fish ??!!

How rude !!
blamocur has commented below his\her name: No free fish here, only free fish lessons.

Telling him/her I want a free fish is like a silly joke. Why did you take it seriously and insisted it is rude? I don't see any rudeness here unless blamocur felt it. Prof. Khan, life is beautiful, don't let Prof. Jomo affects on you. :)
 
blamocur has commented below his\her name: No free fish here, only free fish lessons.

Telling him/her I want a free fish is like a silly joke. Why did you take it seriously and insisted it is rude? I don't see any rudeness here unless blamocur felt it. Prof. Khan, life is beautiful, don't let Prof. Jomo affects on you. :)
@nasi112 I am sorry that my comment has offended you.

That comment was made with my tongue firmly planted in my cheek. I could not find an emoji for that.

It was definitely not aimed at you.

I was not calling you "rude".
 
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