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Hayley Sanders

Hayley Sanders

Answered question

2022-05-20

The integral
cos 12 ( x ) sin 12 ( x ) d x
can be reduced to the form
k sin p ( u ) ( 1 + cos ( u ) ) r ( 1 cos ( u ) ) s d u
by using trigonometric identities and the substitution u = 2 x

Answer & Explanation

Lavizzariym

Lavizzariym

Beginner2022-05-21Added 10 answers

Just multiply and divide by 2 12 . You get
1 2 12 ( 2 sin x cos x ) 12 d x = 1 2 12 sin 12 ( 2 x ) d x
Use u = 2 x, d u = 2 d x. Then the integral becomes
1 2 13 sin 12 ( u ) d u
This is your formula with p = 12 , r = s = 0 , k = 1 / 2 13

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