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∫ sin 4 x d x = …

 

  1. 3 over 4 x minus 1 fourth sin invisible function application 2 x plus 1 over 32 sin invisible function application 4 x plus C 

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

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

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

  5. negative 3 over 8 x minus 1 fourth sin invisible function application 2 x plus 1 over 32 sin invisible function application 4 x plus C 

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

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Pembahasan

Ingat rumus sudut rangkap : Jadi,

Ingat rumus sudut rangkap :

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

Jadi,

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

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