Consider the function h(x)=xcosx defined for x in [−π,π].
(a) Determine whether h is an even function, an odd function, or neither. Support your conclusion algebraically.
(b) Without directly evaluating any antiderivatives, predict the average value of h on [−π,π] and explain your reasoning.
(c) Confirm your prediction by explicitly calculating 2π1∫−ππxcosxdx.