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Pertanyaan

integral 4 sin 3 x sin open parentheses 3 x plus pi over 3 close parentheses d x equals horizontal ellipsis

  1. negative 1 third sin open parentheses 6 x plus pi over 3 close parentheses plus x plus C

  2. negative 1 third sin open parentheses 6 x plus pi over 3 close parentheses plus C

  3. 1 third sin open parentheses 6 x plus pi over 3 close parentheses minus 3 x plus C

  4. 1 third sin open parentheses 6 x plus pi over 3 close parentheses plus x plus C

  5. 1 half sin open parentheses 6 x plus pi over 3 close parentheses plus x plus C

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Ingat rumus :

negative 2 sin A sin B equals cos open parentheses A plus B close parentheses minus cos open parentheses A minus B close parentheses  4 sin 3 x sin open parentheses 3 x plus pi over 3 close parentheses equals negative 2 open parentheses negative 2 sin 3 x sin open parentheses 3 x plus pi over 3 close parentheses close parentheses  equals negative 2 open parentheses cos open parentheses 3 x plus open parentheses 3 x plus pi over 3 close parentheses close parentheses minus cos open parentheses 3 x minus open parentheses 3 x plus pi over 3 close parentheses close parentheses close parentheses  equals negative 2 open parentheses cos open parentheses 6 x plus pi over 3 close parentheses minus cos open parentheses negative pi over 3 close parentheses close parentheses  equals negative 2 open parentheses cos open parentheses 6 x plus pi over 3 close parentheses minus 1 half close parentheses  equals negative 2 cos open parentheses 6 x plus pi over 3 close parentheses plus 1

Jadi,

integral 4 sin 3 x sin open parentheses 3 x plus pi over 3 close parentheses d x equals integral open parentheses negative 2 cos open parentheses 6 x plus pi over 3 close parentheses plus 1 close parentheses d x  equals negative 2 over 6 sin open parentheses 6 x plus pi over 3 close parentheses plus x plus C  equals negative 1 third sin open parentheses 6 x plus pi over 3 close parentheses plus x plus C

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