# PP 8.2 - Trigonometric Integrals In this section we will...

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Trigonometric Integrals

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In this section we will learn how to integrate functions involving trigonometric functions. The table on page 488 contains the six basic integration formulas for trigonometric functions. Review and memorize those formulas.
Tools Needed Trigonometric Identities: 1 cos sin 2 2 = + u u u u 2 2 sec tan 1 = + u u 2 2 csc cot 1 = + ) 2 cos 1 ( sin 2 1 2 u u - = ) 2 cos 1 ( cos 2 1 2 u u + = [ ] [ ] [ ] ) cos( ) cos( cos cos ) cos( ) cos( sin sin ) sin( ) sin( cos sin 2 1 2 1 2 1 B A B A B A B A B A B A B A B A B A + + - = + - - = + + - =

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Examples dx x x ) cos( ) ( sin . 1 3 dx x du x u ) cos( ) sin( = = u-substitution can be used. C x C u du u dx x x + = + = = ) ( sin ) cos( ) ( sin 4 4 1 4 4 1 3 3 dx x ) ( sec . 2 2 C x + = ) tan(
dx x ) ( sin . 3 2 No formula or substitution can be used for this integral. A trigonometric identity is needed. ) 2 cos 1 ( sin 2 1 2 u u - = [ ] - = - = dx x x dx x dx x ) 2 cos( ) 2 cos( 1 ) ( sin 2 1 2 1 2 1 2 du dx dx du x u 2 1 2 2 = = = C x x C u x du u x dx x x dx x + - = + - = - = - = ) 2 sin( ) sin( ) cos( ) 2 cos( ) ( sin 4 1 2 1 4 1 2 1 4 1 2 1 2 1 2 1 2

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dx x ) ( cos . 4 3
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