Introduction to Antiderivatives

AP Calculus · Axiom Academy

Intro Introduction to Antiderivatives Discovering the reverse process of differentiation From Derivatives to Antiderivatives Throughout Unit 3, you learned to answer the question: "Given a function, what is its derivative?" Now we reverse the question entirely. You might quickly guess f(x) = x^2 . But f(x) = x^2 + 5 also works, as does x^2 - 100 or . Every function of the form x^2 + C has derivative 2x . Integration is one of the two pillars of calculus. While derivatives measure rates of change , integrals measure accumulation — the total amount gathered over an interval. Physics: Velocity is the derivative of position. So position is the integral of velocity. Economics: Marginal cost is the derivative of total cost. Total cost is the integral of marginal cost. Biology: Growth rate is the derivative of population. Population is the integral of growth rate. What You'll Learn in This Unit Indefinite integrals — finding antiderivatives with the +C Basic integration rules — power rule, trig, exponential Riemann sums — approximating areas with rectangles Definite integrals — computing exact areas The Fundamental Theorem of Calculus — the bridge between derivatives and integrals U-substitution — the chain rule in reverse Integration by parts (BC) — the product rule in reverse Let's begin the journey into integration!

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