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.

Then, in unison, all the other plumbers say, “Switch the limits on your integral!”

(source)