7.2 Integrals of Trig functions

7.2 Integrals of Trig functions - Z sec(3 z ) tan(3 z ) dz...

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1 7.2 Integrals of Trigonometric Functions. Part I Trigonometric integrals involve combinations of basic trigonometric func- tions. Today, we shall study integrals of the form Case 1: m or n is odd In this case we will use u-substitution along with an identity sin 2 ( x ) + cos 2 ( x ) = 1 Example 1 Z sin 3 ( x ) dx Z sin 4 ( x ) cos 3 ( x ) dx Z sin 3 ( x ) cos 3 ( x ) dx
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2 Example 2 Integrals with tan( x ), cot( x ), sec( x ) or csc( x ) can be evaluated if converted into expressions with sin( x ) and cos( x )
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Unformatted text preview: Z sec(3 z ) tan(3 z ) dz For this one it is easier to apply more direct substitution: Z sec 2 (3 z ) tan(3 z ) dz Z / 8 cot 5 (4 x ) sin 5 (4 x ) dx Case 2: m and n are both even In this case we will use the identities: sin 2 ( ) = cos 2 ( ) = 3 Example 3 Z sin 2 ( x ) dx Z sin 4 ( x ) dx Example 4 To do Z / 3 sin 5 ( x ) dx Z sin 2 ( x ) cos 2 ( x ) dx...
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7.2 Integrals of Trig functions - Z sec(3 z ) tan(3 z ) dz...

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