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Pertanyaan

∫ cos 4 x d x = …

  1. 1 fourth sin 2 x plus 1 over 32 sin 4 x plus C

  2. 3 over 8 x plus 1 fourth sin 2 x minus 1 over 32 sin 4 x plus C

  3. 3 over 8 x minus 1 fourth sin 2 x plus 1 over 32 sin 4 x plus C

  4. 3 over 8 x plus 1 fourth sin 2 x plus 1 over 32 sin 4 x plus C

  5. 3 over 8 x minus 1 fourth sin 2 x minus 1 over 32 sin 4 x plus C

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

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Pembahasan

Ingat rumus sudut rangkap : Jadi,

Ingat rumus sudut rangkap :

cos 2 x equals open curly brackets table row cell 1 minus 2 sin squared x rightwards double arrow sin squared x equals 1 half minus 1 half cos 2 x end cell row cell 2 cos squared x minus 1 rightwards double arrow cos squared x equals 1 half plus 1 half cos 2 x end cell end table close  cos to the power of 4 x  equals cos squared x. cos squared x  equals open parentheses 1 half plus 1 half cos 2 x close parentheses open parentheses 1 half plus 1 half cos 2 x close parentheses  equals 1 fourth plus 1 fourth cos 2 x plus 1 fourth cos 2 x plus 1 fourth cos squared 2 x  equals 1 fourth plus 1 half cos 2 x plus 1 fourth open parentheses 1 half plus 1 half cos 4 x close parentheses  equals 1 fourth plus 1 half cos 2 x plus 1 over 8 plus 1 over 8 cos 4 x  equals 3 over 8 plus 1 half cos 2 x plus 1 over 8 cos 4 x

Jadi,

integral cos to the power of 4 x d x equals integral open parentheses 3 over 8 plus 1 half cos 2 x plus 1 over 8 cos 4 x close parentheses d x  equals 3 over 8 x plus 1 half.1 half sin 2 x plus 1 over 8.1 fourth sin 4 x plus C  equals 3 over 8 x plus 1 fourth sin 2 x plus 1 over 32 sin 4 x plus C

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