I have a question about line integrals,
Q: Evaluate the line integral,
$$\int_C(2ye^{x^2-z}\cos(y^2)-9xy^2)dy+(12z-e^{x^2-z}\sin(y^2))dz+(2xe^{x^2-z}\sin(y^2)-3y^3)dx$$
Where C is the broken line from $A(0, \sqrt{\pi}, 3)$ to $B(0, \sqrt{\frac{\pi}{2}}, -1)$ connecting $(0, \sqrt{\pi}, 3)$, $(1,3,5)$, $(0,\sqrt{\frac{\pi}{2}},-1)$.
I could solve this question if it was given a curve but I can't figure out how to solve this.
I tried to use the method on this question but I couldn't parametrize the lines.
How can I solve this question?
Thanks!
Best Answer
The vector field is conservative with potential
$$f(x,y,z) = e^{x^2-z}\sin(y^2)-3xy^3+6z^2$$
Can you take it from here?