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Pertanyaan

Nilai integral subscript 0 superscript pi over 2 end superscript cos 2 x sin x space d x equals horizontal ellipsis

  1. negative 2 over 3

  2. negative 1 third

  3. 0

  4. 1 third

  5. 2 over 3

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Ingat rumus 2 cos A sin B equals sin open parentheses A plus B close parentheses minus sin open parentheses A minus B close parentheses

cos 2 x sin x equals 1 half open parentheses 2 cos 2 x sin x close parentheses  equals 1 half open parentheses sin open parentheses 2 x plus x close parentheses minus sin open parentheses 2 x minus x close parentheses close parentheses  equals 1 half sin 3 x minus 1 half sin x    integral subscript 0 superscript pi over 2 end superscript cos 2 x sin x space d x equals integral subscript 0 superscript pi over 2 end superscript open parentheses 1 half sin 3 x minus 1 half sin x close parentheses space d x  equals negative 1 over 6 cos 3 x plus 1 half cos x open table row cell pi over 2 end cell row 0 end table close square brackets  equals open parentheses negative 1 over 6 cos 3 open parentheses pi over 2 close parentheses plus 1 half cos open parentheses pi over 2 close parentheses close parentheses minus open parentheses negative 1 over 6 cos 3 open parentheses 0 close parentheses plus 1 half cos open parentheses 0 close parentheses close parentheses  equals open parentheses 0 close parentheses minus open parentheses negative 1 over 6 plus 1 half close parentheses  equals negative 1 third

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