The Fundamental Theorem of Calculus Made Simple

The Fundamental Theorem of Calculus (FTC) shows how two important ideas in math, derivatives and integrals, work together. This theorem helps us find the area under curves. But, understanding this can be tough for many students.

1. What Are Derivatives and Integrals?

   • A derivative tells us how fast something is changing.
   • An integral helps us add up areas.
   • Switching between these two ideas can be challenging.

2. How to Calculate Area Under a Curve

   • To find the area under a curve called $f(x)$ between points $a$ and $b$, we use an integral: $\int_a^b f(x) \, dx$.
   • The FTC says that if $F$ is a function that helps us find the area, then we can calculate it like this: $\int_a^b f(x) \, dx = F(b) - F(a)$.

If you find this tricky, don’t worry! You can get better with practice, visual tools, and some cool number techniques.