Integrals#
Indefinite integrals#
Description |
Equations |
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Indefinite integral (antiderivative) |
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Antiderivative as a family of functions |
If |
Table of indefinite integrals#
Function |
Antiderivative |
Function |
Antiderivative |
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Definite integrals as Riemann sums#
Description |
Equations |
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Area |
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Definite integral |
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Operational definition of definite integral as Riemann sum |
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Properties of definite integrals#
Description |
Equations |
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Reversing the bounds changes the sign of definite integrals |
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Definite integral is zero if upper and lower bounds are the same |
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Definite integrals of constant |
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Addition and subtraction of definite integrals |
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Constant multiple of definite integrals |
Fundamental theorem of calculus#
Description |
Equations |
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Fundamental Theorem of Calculus I |
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Fundamental Theorem of Calculus II |
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Net Change Theorem |
Substitution rule#
Description |
Equations |
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Substitution rule (u-substitution) |
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Substitution rule for definite integrals |
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Integrals of even functions |
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Integrals of odd functions |
Techniques of Integration#
Integration by parts#
Description |
Equations |
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Integration by parts |
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Integration by parts |
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Integration by parts for definite integrals |
Trigonometric integrals#
Description |
Equations |
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Integral of even power of sine and cosine using trig identities |
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Trig identity for solving |
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Trig identity for solving |
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Trig identity for solving |