I received the following email: I can't see the logic in assuming (for example) that a function containing sqrt (a^2 - x^2) in the integrand would lead you to substitute x with a trig reference. Why a trig reference? What connection does the integrand, trig-less function have to trigonometry? To me, it seems about as rational as replacing the 'a' with pi, or e, or a sausage! How can I make this tangible? Are there any online illustrations of this?