Determine whether each of the following line integrals is

Last updated: 4/29/2023

Determine whether each of the following line integrals is indepen dent of path If it is find a function h such that dh P dx Qdy If it is not find a closed pathy around which the integral is not zero a x dx ydy b x dx y dy c y dx xdy d y dx x dy Solution We compute the partial derivatve because if h exist we have that dh Pdx Qdy where OP ay 0Q dx a b P r OP dy 0 Pdx 9 y h 2 y P x aP 0 y Q y 39 0 dr fQdy f x Q y aQ 0 da f Pdx 9 y Qdy f x 6 h 22 y 6