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1d
comment Line integral and checking its path independence in three dimensions
Thank you for the edited answer. 1) Did you get $U(1,0,0)$ by substituting $12 \pi$ (and then 0) into $\gamma(t)=(\cos^{4}t,\cos t\sin^5t,\sin^4t)$? 2) Could the task be finished after this substitution, since the $\gamma$ is a closed curve? 3) What if the $\gamma$ is not a closed curve?
1d
accepted Line integral and checking its path independence in three dimensions
2d
comment Line integral and checking its path independence in three dimensions
Thank you for the answer. I have two questions regarding it: 1) Why did you write that $g$ is a constant and not $0$? 2) Why did you substitute $(1,0,0)$ under $U$? 3) Then why do I need the info about $\gamma(t)=(\cos^{4}t,\cos t\sin^5t,\sin^4t)$ and $t \in[0,12\pi]$ in the exercise?
2d
comment Line integral and checking its path independence in three dimensions
Yes $P′x$ is the partial derivative of $P$ with respect to $x$. How did I get to $U=xycos(yz)$? You are right, I confused $U_{y}$ with $U$. How should I continue?
2d
asked Line integral and checking its path independence in three dimensions
2d
awarded  Informed
Aug
22
awarded  Scholar
Aug
22
accepted Finding the mass of a curve having a specified linear density using a line integral
Aug
22
comment Finding the mass of a curve having a specified linear density using a line integral
Thank you very much. Now I understand why wolfram was giving me 0. Apparently my computation was right despite the mistake with the absolute value.
Aug
22
asked Finding the mass of a curve having a specified linear density using a line integral
Dec
18
awarded  Supporter
Dec
18
comment Finding volume of a shape using double integral
Thank You, what program do You use for that?
Dec
18
awarded  Student
Dec
18
asked Finding volume of a shape using double integral