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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?
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?
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.
Dec
18
comment Finding volume of a shape using double integral
Thank You, what program do You use for that?