Suppose that a nonnegative function y = (x) has a continuous first derivative on [a, b]. Let C be the boundary of the region in

Suppose that a nonnegative function y = ƒ(x) has a continuous first derivative on [a, b]. Let C be the boundary of the region in the xy-plane that is bounded below by the x-axis, above by the graph of ƒ, and on the sides by the lines x = a and x = b. Show that

So a f(x) dx -fydr. C