Originally Posted by
n22 Hi I am not sure if i am doing this right.The question im having issues with is in green text.
The text in blue are the other parts of the question(I included it because it may be necessary...but was easy to calculate.)..
F is a force field . F=2xyzi+ (x²z+2y)j+(x²y-2z)k
Calculate ∇xF,and show its conservative.
find potential function Φ for F,
Hence find the work done by F.around the closed curve x²+y²=1 in the plane z=0, transversed in a counterclockwise direction ,starting and ending at the point (1,0,0)
(Clearly this is the base of a cylinder.)
Here is my method :
letting x=costi (α)
y=sintj
since x²+y²=1,y=√1-x² (β)
then subbing (α) into (B)
I got r=sin²ti+cos²tj=1 t ranges from 0 to 2π
then dr=(2sintcost)idt-(2costsint)jdt