Integration and Differentiation Theory

Integration and differentiation are fundamental concepts in calculus. Differentiation measures how a function changes at a specific point—essentially calculating its slope or rate of change. Conversely, integration sums small parts to find the whole—like calculating the total area under a curve. Think of differentiation as analyzing how quickly something changes, while integration assesses the accumulation or total quantity resulting from continuous change. Together, these concepts describe dynamic systems, enabling us to understand motion, growth, and other phenomena by examining both their rates and totals.