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Pertanyaan

∫ 0 6 1 ​ π ​ 4 sin 7 x . cos 3 x d x = …

  1. negative 3 over 20

  2. negative 13 over 10

  3. negative 5 over 7

  4. 13 over 10

  5. 17 over 20

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

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Pembahasan

Ingat rumus : Jadi,

Ingat rumus :

2 sin A cos B equals sin open parentheses A plus B close parentheses plus sin open parentheses A minus B close parentheses  4 sin 7 x cos 3 x  equals 2 open parentheses 2 sin 7 x cos 3 x close parentheses  equals 2 open parentheses sin open parentheses 7 x plus 3 x close parentheses plus sin open parentheses 7 x minus 3 x close parentheses close parentheses  equals 2 sin 10 x plus 2 sin 4 x

Jadi,

integral subscript 0 superscript 1 over 6 pi end superscript 4 sin 7 x. cos 3 x space d x equals integral subscript 0 superscript 1 over 6 pi end superscript open parentheses 2 sin 10 x plus 2 sin 4 x close parentheses space d x  equals negative 2 over 10 cos 10 x minus 2 over 4 cos 4 x open table row cell 1 over 6 pi end cell row 0 end table close square brackets  equals negative 1 fifth cos 10 x minus 1 half cos 4 x open table row cell 1 over 6 pi end cell row 0 end table close square brackets  equals negative 1 fifth cos 10 open parentheses 1 over 6 pi close parentheses minus 1 half cos 4 open parentheses 1 over 6 pi close parentheses minus open parentheses negative 1 fifth cos 10 open parentheses 0 close parentheses minus 1 half cos 4 open parentheses 1 over 6 pi close parentheses close parentheses  equals negative 1 fifth open parentheses 1 half close parentheses minus 1 half open parentheses negative 1 half close parentheses minus open parentheses negative 1 fifth open parentheses 1 close parentheses minus 1 half open parentheses 1 close parentheses close parentheses  equals negative 1 over 10 plus 1 fourth plus 1 fifth plus 1 half equals 17 over 20

11

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