26 lines
735 B
Markdown
26 lines
735 B
Markdown
---
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id: mat-04-integrals
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title: "Integrals: basics and the fundamental theorem"
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---
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# Integrals
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## Antiderivative
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An antiderivative is a function whose derivative is the integrand.
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## Definite integral
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A definite integral measures accumulated change and is interpreted as signed area under a curve.
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## Fundamental theorem of calculus
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The fundamental theorem connects derivatives and integrals:
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- differentiation and accumulation are inverse operations (under suitable conditions)
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## Basic integration rules
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Rules include:
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- linearity
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- power rule for integrals (with n not equal to -1)
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- integral of 1/x is ln|x|
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## Substitution idea
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Substitution changes variables to simplify the integrand when a composition structure appears.
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