What does area have to do with slope? | Chapter 9, Essence of calculus

This video, titled "What does area have to do with slope? | Chapter 9, Essence of calculus," is by the channel "3Blue1Brown" and was published on May 6, 2017. It's an educational video exploring why integrals and derivatives are inverses of each other. The video discusses the concept of the average of a continuous variable and how to calculate it using integrals. For example, it calculates the average height of the sine function graph over the interval from zero to pi (half its period). This concept is illustrated using the principles of integrals and derivatives. To calculate the average, the integral of the function over the desired interval is first computed and then divided by the length of the interval. This process demonstrates how the average height of a graph is related to the area under the graph and its slope. The video also connects the concept of average in continuous variables to the conventional average in discrete variables. This connection is explained through the concept of integrals and derivatives, showing why integrals and derivatives are inverses of each other. Finally, the video explains how concepts applicable to discrete variables can be extended to continuous variables and how integrals can be used to solve problems related to continuous variables.