FocusFront Integrals

Integrals are a fundamental concept in calculus that represent the accumulation of quantities, such as areas under curves, total distances traveled, or accumulated quantities over time. The process of integration is the inverse of differentiation, and it plays a crucial role in understanding how quantities change and accumulate in various contexts.

• Geometrically, integration can be interpreted as the area under a curve or the accumulation of a quantity over an interval. For a continuous function f(x)f(x) f ( x ) , the definite integral represents the total area between the graph of f(x)f(x) f ( x ) and the x-axis, within the given limits.
• Physically, integration is often used to find quantities such as distance, work, or mass, where the integrand represents a rate of change (e.g., velocity, force, density).