On November 11, 1675, Leibniz demonstrated this for the first time by using the integral symbol ( ∫integral of
Think of a wine barrel. Johannes Kepler once tried to calculate its volume by imagining the wine was made of infinitely many, infinitely thin disks stacked on top of each other. By "summing" the areas of all those thin disks, he found the volume of the whole container. Introduction to integral Calculus
Centuries later, in the 1600s, Gottfried Wilhelm Leibniz and Isaac Newton independently discovered that integration was actually the "undoing" of differentiation. While differential calculus looks at the (like how fast a car is going right now), integral calculus looks at the accumulation (how much distance the car has covered in total). On November 11, 1675, Leibniz demonstrated this for
This is the story of how humans learned to calculate the "uncalculable"—from measuring the curve of a circle to tracking the exact distance a car travels as its speed constantly shifts. The Problem: Beyond Straight Lines Centuries later, in the 1600s, Gottfried Wilhelm Leibniz
Today, we use this same logic—formally called a —to calculate everything from the trajectory of a rocket to the growth of a bacterial population.