Ok the qu is:
Write down a condition obeyed by a conservative vector field V= {P(x,y), Q(x,y)}
This must be that (dP/dy)=(dQ/dx) so that the differential equation would be exact. But for the case:
P= (x^2)y + y Q= x(y^2) + x
if using (dP/dy)=(dQ/dx) then this isnt exact but is using (dP/dx)/(dQ/dy) then it is, and as the question does not actually specify which function is dx and which is dy, then which one should i use to find a function f(x,y) such that V= (upside down triangle)f ?
Also, how would i evaluate the line integrals:
C1 : x=t, y=t (0<t<1)
C2: x=0, y=t (0<t<1); x=t, y=1 (0<t<1)
for integral of Pdx+ Qdy as stated above
I realise for this case the differential equation is not exact, so should i assume this for the beginning of the question, and assume that the vector field is not conservative?
thanks v much for ne help,
Ellie