General Formula for the Area Under a Curve | From Riemann Sums to Definite Integrals

📚 General Formula for the Area Under a Curve | Calculus 1 In this video, we’ll derive the general formula for finding the area under a function y = f(x) from x = a to x = b. You’ll see how the idea of adding up rectangles leads to the definition of the definite integral. This is where we move from estimating area to finding the exact area under a curve using limits. 🔍 What You’ll Learn in This Video: ✅ How to represent area using rectangles ✔ Definition of Δx = (b – a)/n and xᵢ = a + iΔx ✔ Writing the Riemann sum formula for area ✔ Transitioning from an approximate area to an exact area ✔ The connection between Riemann sums and definite integrals 📥 Download Free Guided Notes! 👉 https://www.understandthemath.com/cal... Limits and Derivatives    • The Tangent Problem and the Velocity Probl...      • The Limit of a Function| Intuitive, Genera...      • How to Calculate Limits Using Limit Laws |...      • Precise Definition of a Limit (Epsilon–Del...      • Understanding Continuity in Calculus: Defi...      • Limits at Infinity and Horizontal Asymptot...      • Derivatives and Rates of Change in Calculu...      • The Derivative as a Function: Graphing, Di...      • The Derivative as a Function: Graphing, Di...   Differentiation Rules    • Derivatives of Polynomials and Exponential...      • Product Rule and Quotient Rule in Calculus...      • Derivatives of Trigonometric Functions: Si...      • The Chain Rule in Calculus: How to Differe...      • Implicit Differentiation in Calculus: Step...      • Derivatives of Inverse Trigonometric Funct...      • Derivatives of Logarithmic Functions and L...      • Rates of Change in Calculus | Physics, Che...      • Exponential Growth and Decay | Population,...      • Related Rates in Calculus | 8 Classic Exam...      • Linear Approximation and Differentials in ...      • Hyperbolic Functions in Calculus | Definit...   Applications of Differentiation    • Maximum and Minimum Values in Calculus | C...      • The Mean Value Theorem in Calculus | Expla...      • How Derivatives Affect the Shape of a Grap...      • L’Hôpital’s Rule in Calculus | Indetermina...      • Curve Sketching in Calculus | Step-by-Step...      • Graphing with Calculus and Technology | Us...      • Optimization Problems in Calculus | Step-b...      • Newton’s Method Explained | Approximating ...      • Antiderivatives | Definition, Formulas, an...   Integrals    • The Area Problem | Approximating and Findi...   Visit the Understand The Math Website https://www.understandthemath.com Find free guided notes, filled in guided notes for purchase, course playlists, and math merchandise. Connect & Support TikTok:   / understandthemath   Instagram:   / understandthemath   Facebook: https://www.facebook.com/profile.php?... Support: https://buymeacoffee.com/understandth... More About Understand The Math Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples. Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective. #Calculus #Calculus1 #RiemannSums #AreaUnderCurve #DefiniteIntegral #IntegralFormula #CalculusExamples #UnderstandTheMath #MathVideo #GuidedNotes