Lesson 1: Preview
Think about the area of a circile. We know that it’s area is $\pi R^2$. But, why?
We can solve the problem this way. Imagine that we divide a radius of this circle into many smaller pieces, each with a width of $dr$. Then this circle will be composed of many rings. If we tear a ring open and flatten it, it will become a rectangle-ish shape. The length of this “rectangle” is the circumference of this ring and the width is $dr$. The area of this ring is the area of this …