Fundamental Theorem of Calculus Part 1

AP Calculus · Axiom Academy

Lesson Fundamental Theorem of Calculus Part 1 The connection between derivatives and integrals — FTC Part 1 The Most Important Theorem in Calculus The Fundamental Theorem of Calculus (FTC) connects the two main operations of calculus: differentiation and integration. Part 1 tells us that differentiation undoes integration. If f is continuous on [a,b] and , then: FTC Part 1 says that if you define a function by accumulating area under f(t) from a fixed starting point a to a variable endpoint x , then the derivative of that accumulation function is simply f(x) itself. When the upper limit is g(x) , multiply by g'(x) (chain rule) This theorem tells us every continuous function has an antiderivative The variable of integration ( t ) is a "dummy variable" — the result depends on x

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