Integrals: From Area to Riemann Sums Mastery

Ever wondered how we calculate the exact area under a curvy graph? It's not just about rectangles; it's a journey from visual estimation to precise mathematical definition! In AP Calculus, we'll explore how the concept of an integral evolves from approximating areas with shapes to defining it rigorously using Riemann sums and limits. Get ready to unlock the secrets of integration, a fundamental tool in calculus with applications in physics, engineering, and economics. This article will guide you through:

• The intuitive idea of area under a curve
• Approximating area using Riemann sums
• Defining the definite integral as a limit
• Connecting Riemann sums to integral notation