What is an integral and how does it add up tiny pieces?
Slice & Sum
What is an integral and how does it add up tiny pieces?
Suppose you want to know the area of a wobbly puddle on the sidewalk. A square is easy — length times width, done. But a puddle has curves, bulges, a little spilly tail. There's no neat formula for "puddle." So what do you do? You cheat in the cleverest way ever invented. You chop the puddle into pieces so tiny they may as well be straight.
Here's the trick. Lay a grid of skinny rectangles across the puddle, like floorboards. Each rectangle is simple — it has a width and a height, so its area is easy. Sure, the rectangles don't fit the curves perfectly. They stick out a little here, fall short a little there. But if you add up all their areas, you get a rough guess for the whole puddle.
