❖ The Definite Integral - Understanding the Definition ❖

The Definite Integral: Understanding the Definition
In this video, we dive deep into the definition of the definite integral, exploring its conceptual meaning and breaking down the limit process involved in defining the integral. By understanding how the sum of the areas of rectangles approaches the area under a curve as the number of rectangles increases, we build the foundation for understanding what a definite integral represents. Note that this video focuses on the theory and definition, rather than the computation of definite integrals.

What You Will Learn:
The definition of the definite integral and its connection to the area under a curve.
How to interpret the limit of Riemann sums as a way to understand the integral.
The process of dividing an interval into subintervals and evaluating the function at sample points.
A conceptual understanding of how the integral is built from sums of areas.
📚 Check out my book: 1001 Calculus Problems for Dummies for more practice!

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[IDidactI]

When you differentiate, you divide a tiny slice of y by a tiny slice of x i.e. dy/dx. That ratio gives you a slope, which hopefully you understand. So, dy/dx = f'(x). Okay so what happens if we multiply both sides of that by dx, we get dy = f'(x) * dx. So to find y, add up all the 'dy's. That's what the integral does. Also, look at the equation. f'(x) is the height of the function and dx is the width. Area of a rectangle = height * width, right? You can figure out the rest ;)

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