Definite Integrals Explained: Riemann Sums, Signed Area, and Properties

Master the concept of definite integrals in this comprehensive XO Math video lesson. We’ll build your understanding from the ground up—starting with Riemann sums, the formal definition of a definite integral, and the idea of signed area. You'll learn how to: Use graphical representations and geometry to evaluate definite integrals Understand the properties and notation of definite integrals Apply symmetry (even/odd functions) to simplify integrals Use the comparison theorem to bound definite integrals Solve step-by-step examples involving line segments, absolute value functions, semicircles, and more This lesson connects the ideas of limits, antiderivatives, and area under a curve to give you a full picture of how definite integrals work in calculus. For more video lessons and additional resources, visit www.xomath.com.