Show that the line integral is independent of path. 2xe -Ydx + (2y - x2e-V)dy, C is any path from (1, 0) to (4, 1) The functions 2xe- and 2y - xzey have continuous first-order derivatives on R2 and - (2xe-y) = = ( 2y - x2 e - y) , SO F ( X, y) = i + (2y - xe -/) j is a ax conservative vector field by the theorem given below, hence the line integral is independent of path. Theorem: Let F = Pi + Qj be a vector field on an open simply-connected region D. Suppose that P and Q have continuous first-order partial derivatives and = do throughout D. Then ay ax F is conservative. Evaluate the integral