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Pertanyaan

∫ ​ sin 3 ( x − 2 π ) d x = ...

  1. cos left parenthesis x minus 2 straight pi right parenthesis minus 1 third cos cubed left parenthesis x minus 2 straight pi right parenthesis plus C

  2. cos space left parenthesis x minus 2 straight pi right parenthesis plus 1 third cos cubed left parenthesis x minus 2 straight pi right parenthesis plus C

  3. negative cos left parenthesis x minus 2 straight pi right parenthesis minus 1 third cos cubed left parenthesis x minus 2 straight pi right parenthesis plus C

  4. negative cos left parenthesis x minus 2 straight pi right parenthesis plus 1 third cos cubed left parenthesis x minus 2 straight pi right parenthesis plus C

  5. negative 2 x cubed cos left parenthesis x minus 2 straight pi right parenthesis plus 1 third cos cubed open parentheses x minus 2 straight pi close parentheses plus C

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

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Pembahasan

Gunakan identitas trigonometri berikut ini untuk merubah Misalkan:

Gunakan identitas trigonometri berikut ini untuk merubah sin squared A space colon

sin squared A plus cos squared A equals 1

Misalkan:

u equals space cos space left parenthesis x minus 2 straight pi right parenthesis  du space equals sin space left parenthesis straight x minus 2 straight pi right parenthesis space dx    maka comma  integral subscript blank sin cubed open parentheses straight x minus 2 straight pi close parentheses dx space equals integral subscript blank sin space left parenthesis straight x minus 2 straight pi right parenthesis space sin squared space left parenthesis straight x minus 2 straight pi right parenthesis dx  equals integral subscript blank sin space left parenthesis straight x minus 2 straight pi right parenthesis left square bracket 1 minus cos squared left parenthesis straight x minus 2 straight pi right parenthesis right square bracket dx  equals integral subscript blank left square bracket sin space left parenthesis straight x minus 2 straight pi right parenthesis minus sin space left parenthesis straight x minus 2 straight pi right parenthesis cos space squared left parenthesis straight x minus 2 straight pi right parenthesis right square bracket space dx  equals integral subscript blank sin space left parenthesis straight x minus 2 straight pi right parenthesis dx minus integral cos squared left parenthesis straight x minus 2 straight pi right parenthesis space sin space left parenthesis straight x minus 2 straight pi right parenthesis dx  equals integral subscript blank sin space left parenthesis straight x minus 2 straight pi right parenthesis space dx minus integral subscript blank straight u squared du  equals negative cos space left parenthesis straight x minus 2 straight pi right parenthesis minus 1 third straight u cubed plus straight C  equals negative cos space left parenthesis straight x minus 2 straight pi right parenthesis minus 1 third cos cubed left parenthesis straight x minus 2 straight pi right parenthesis plus straight C

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