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Fundamental Theorem of Calculus
★★★☆☆High School
📖Definition
The Fundamental Theorem of Calculus shows differentiation and integration are inverse operations. It allows computing definite integrals via antiderivatives.
📐Formulas
(d)/(dx) ∈tₐ^x f(t) dt = f(x)
First Fundamental Theorem
∈tₐ^b f(x) dx = F(b) - F(a)
Second Fundamental Theorem (F' = f)
✏️Examples
예제 1
Calculate ∫₀² 3x² dx using the theorem.
📜History
Discovered by: Newton, Leibniz (1660s)
Discovered independently by Newton and Leibniz; core of calculus.
⚡Applications
Physics
Equations of motion
Engineering
Area, volume calculation
Economics
Total cost, revenue
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