1. ## Line integral

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.

2. ## Re: Line integral

how did you show it was a conservative vector field. Use this fact,

if $\displaystyle \nabla G = F$ then $\displaystyle \int_{C} F dr = G(b) - G(a)$

3. ## Re: Line integral

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.

4. ## Re: Line integral

For the second problem, in order to find the normal vector I would take the partial derivs of G(theta, phi) in terms of theta and phi, then take the cross product correct? If so, what are the bounds for?