how did you show it was a conservative vector field. Use this fact,
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(3t16 - 9t13 - t11 + 12t10 +8t8 -2t6 -14t5 -3t4 +t3 +3t +2))/(t12 -2t7 +t2 +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.