Understanding Indefinite Integrals
In calculus, an indefinite integral is the antiderivative of a function. It's represented as:
∫ f(x) dx = F(x) + C
where F(x) is a function whose derivative is f(x), and C represents an arbitrary constant, which appears because the process of differentiation loses this constant information.
Importance and Applications
Indefinite integrals are foundational in solving differential equations, determining areas under curves, and are pivotal in physics for calculating quantities like displacement from velocity functions. See our detailed exploration on applications of calculus.
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