🔴 Introduction to INTEGRALS: Key concepts, table, and properties

Hello, how are you? Okay everyone, let's start with integrals, which is one of the most important topics in any analysis course. Remember when we covered derivatives, and I told you that you can't pass analysis without knowing how to differentiate? Well, today with integrals, I'm telling you the same thing, and let's start like this: you can't pass this analysis class without knowing how to integrate. So that's what we're going to learn to do now, and the first key concept I want you to take away from this class today is that we can think of integrating and differentiating as opposite operations. That is, just like, for example, adding and subtracting, or multiplying and dividing, well, something analogous exists between differentiating and integrating. In fact, you will often hear the expression that the integral is called the antiderivative. That is, for example, if you have a function $F$, and I tell you that I added two to the function and then subtracted two...