“우리 대부분은 초라한 옷차림과 엉터리 가구들을 부끄럽게 여기지만, 초라한 생각과 엉터리 철학을 부끄럽게 여길 줄 알아야 한다.” – Albert Einstein

19900101
calculus integrals

https://www.eeweb.com/tools/calculus-integrals-sheet

#### Definition of an Integral

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.

where     and

where

#### Integration by Trigonometric Substitution

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

##### First Trigonometric Substitution

To take advantage of the property

Substitute

After substitution

##### Second Trigonometric Substitution

To take advantage of the property

Substitute

After substitute

##### Third Trigonometric Substitution

To take advantage of the property

Substitute

After substitute

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