Definite Integrals Introduction
It's time to answer the burning question that every calculus student asks. How does all of this "calculus" stuff relate to geometry? No? That question hasn't come to mind? Maybe we're trying to plant thoughts in your head, Big Brother style. Either way, calculus does relates to geometry. This section will be dedicated to areas. Area under the curve, area of a triangle, Area 51, definite integrals can be used to solve them all; maybe not the alien thing.
If you aren't convinced about the super usefulness of definite integrals—drumroll— they can also be used to calculate volumes. That's right. You want to know how much water fits in your grandma's vase? Integrate that vase. How much cheese is actually in the wheel? Integrate that cheese.
In this unit we'll show you tons of ways to approximate funny-shaped areas. Some areas we'll be able to find exactly. We'll tell you what integrals are and useful things you can do with them.