how did you show it was a conservative vector field. Use this fact,
if then
Hey i am working on problem number 1 here, and showed that it is a conservative vector just fine. However, when i solve for the integrand using f(c(t)) dot c'(t), I get an extremely long polynomial over a fraction, and taking the integral of this seems kind of unreasonable, especially since we are not allowed calculators. The integral is :
(-2t(3t^{16} - 9t^{13 }- t^{11 }+ 12t^{10 }+8t^{8 }-2t^{6 }-14t^{5 }-3t^{4} +t^{3 }+3t +2))/(t^{12} -2t^{7 }+t^{2 }+1)^{2}
I did the integral on wolfram and got -1, but i feel like i am doing something wrong.
Oh wow thanks alot im an idiot...
I showed it was conservative by taking the partial derivatives of the x component of the vector in terms of y, then taking the partial deriv of the y component in terms of x and checking if they were equal to each other, which they were.