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Calculus Integrals Math Sheet

An Engineers Quick Calculus Integrals Reference

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Integrals Definition of an Integral Properites Common Integrals Integration by Subs. Integration by Parts Integration by Trig. Subs. Second Trig. Subs. Third Trig. Subs.

Integrals

Definition of an IntegralReturn to Top

The integral is a mathematical analysis applied to a function that results in the area bounded by the graph of the function, x axis, and limits of the integral. Integrals can be referred to as anti-derivatives, because the derivative of the integral of a function is equal to the function.

ProperitesReturn to Top

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Common IntegralsReturn to Top

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Integration by SubstitutionReturn to Top

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Integration by PartsReturn to Top

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Integration by Trigonometric SubstitutionReturn to Top

Trigonometric identities can be use with integration substitution to simplify integrals. There are three common substitutions.

First Trigonometric SubstitutionReturn to Top

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To take advantage of the property

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Substitute

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After substitution

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Second Trigonometric SubstitutionReturn to Top

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To take advantage of the property

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Substitute

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After substitute

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Third Trigonometric SubstitutionReturn to Top

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To take advantage of the property

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Substitute

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After substitute

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