Recent content by ZARATHUSTRA

It was my bad and hasty interpretation. But the Book name is Calculus Early Transcendentals(2nd E) by Briggs Cochran Gillett

Thank you so much sir, I think I get it now.

so I guess the statement "if the Line integral of an enclosed curve is zero, then the vector field must be conservative." is false

hmm maybe I interpreted wrong

yes of course, the integral I calculated from your region is definitely NOT zero. But the region I calculated IS zero, and the region is still closed curve. But the textbook tells me that if the Line integral of an enclosed curve is zero, then the vector field must be conservative.

and if The region I calculated is a closed curve and it is zero, then it should be conservative, right?

right, but I was calculating the line integral of a circle centered at (0,0,0)

sorry about that, I will, I was very anxious.

but this doesn't describe the circle, does it?

what do you mean it vanishes? is my line integral zero?

but I just can't find where I calculated wrong

right, but the enclosed line integral is zero, which means either I am wrong with the integral calculation, or the vector field is conservative

Thanks in advance for anyone who takes time to read it and would like to help me with the problem

cant find anything wrong with my calculation process and the textbook tells me that if enclosed line integral is zero then vector field must be conservative which means there is something with my work but I checked my work so many times and I just can't find it

dr(t)/dt=(-sint,cost) then dot with F gets -(sintcos^2t)