(915, #19) Show that the line integral

where C is any path from (-1,0) to (5,1) is independent of the path and evaluate the integral.

Solution: First,

is conservative, for we have:

Finding a potential f:

Thus F(x,y) has the potential
f, so is conservative, so line integrals of F will be independent
of path. Next, the given integral is a line integral of F and

by C.A.H.