Louis La Minh Hoang

In this math lesson, I worked on integration, starting from the simple and foundational ideas before moving on to slightly more involved applications. The goal was to build a clear understanding of what integration actually represents, not just how to perform it mechanically.

We began with basic integrals of common functions, treating integration as the reverse process of differentiation. This helped connect new ideas with what I had already learned, making the rules feel more natural rather than memorized. Understanding how powers change and why constants appear in the result was an important part of this stage.

We also discussed the meaning of the constant of integration and why it must always be included when finding an indefinite integral. Instead of seeing it as an annoying extra symbol, we linked it to the idea that many different functions can have the same derivative.

Simple applications were introduced as well, especially interpreting integration as the area under a curve. Even at this basic level, it required careful thinking about limits and the shape of graphs, reinforcing the connection between algebra and geometry.

Although the content was introductory, this lesson laid the groundwork for more advanced integration techniques later on. By starting with simple cases and focusing on understanding, integration began to feel like a logical extension of differentiation rather than a completely new and separate topic.