The Math Professor Plumber A math professor has a problem with his plumbing, so he hires a plumber. He watches the plumber use a wrench to tighten a joint, then is handed a bill for a couple hundred dollars. ""I had no idea that plumbers made this much money!"" he said, ""I've been a math professor for 20 years and I can't claim to make this much per hour."" So the professor decides to become a plumber and for a while he's very happy. Then the licensing board decides that plumbers need to know more math, and the professor, along with all the other plumbers, have to attend a math class. The teacher called on him one day to go to the board and compute the circumference of a circle. The professor gets to the board, but for some reason, he can't remember the formula to determine the circumference. So he decides to derive the formula. The professor fills the board with calculations, but at the end he gets a formula that he knows is incorrect. Figuring he made a mistake somewhere along the line, he erases all his calculations and starts again, but again he gets the same incorrect answer. He's stumped! He stares at the blackboard and tries to figure out what he's doing wrong. He is frustrated. He looks a bit scared at the class and sees all the plumbers whisper, pass notes and hears his closest friend hiss: ""Switch the limits of the integral!!""