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space space integral subscript 0 superscript 1 over 6 straight pi end superscript sin 3 x space sin x space d x equals...

  1. 1 over 8 left parenthesis square root of 3 minus 2 right parenthesisspace space

  2. 1 fourth left parenthesis square root of 3 minus 2 right parenthesisspace space

  3. 1 over 8 left parenthesis 2 minus square root of 3 right parenthesisspace space

  4. 1 fourth left parenthesis 2 minus square root of 3 right parenthesisspace space

  5. 1 over 8 left parenthesis square root of 3 plus 2 right parenthesisspace space

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Diketahui : 

  • space space integral subscript 0 superscript 1 over 6 straight pi end superscript sin 3 x space sin x space d x

Jawab :

sebelum kita menyelesaikan integral tersebut, terlebih dahulu kita ubah bentuk integral tersebut dengan menggunakan rumus sebagai berikut,

sin A. sin B equals negative 1 half open parentheses cos left parenthesis A plus B right parenthesis minus cos left parenthesis A minus B right parenthesis close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell sin 3 x. sin x end cell equals cell negative 1 half open parentheses cos left parenthesis 3 x plus x right parenthesis minus cos left parenthesis 3 x minus x right parenthesis close parentheses end cell row blank equals cell negative 1 half open parentheses cos left parenthesis 3 x plus x right parenthesis minus cos left parenthesis 3 x minus x right parenthesis close parentheses end cell row blank equals cell negative 1 half open parentheses cos left parenthesis 4 x right parenthesis minus cos left parenthesis 2 x right parenthesis close parentheses end cell end table

sehingga didapat bentuk integral baru,

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 0 superscript 1 over 6 straight pi end superscript sin 3 x space sin x space d x end cell row blank equals cell integral subscript 0 superscript 1 over 6 straight pi end superscript left parenthesis negative 1 half cos 4 x plus 1 half cos 2 x right parenthesis d x end cell row blank equals cell open vertical bar 1 over 8 sin 4 x minus 1 fourth sin 2 x close vertical bar subscript 0 superscript 1 over 6 straight pi end superscript end cell row blank equals cell open parentheses 1 over 8 sin 4 open parentheses 1 over 6 straight pi close parentheses minus 1 fourth sin 2 open parentheses 1 over 6 straight pi close parentheses close parentheses minus open parentheses 1 over 8 sin 4 open parentheses 0 close parentheses minus 1 fourth sin 2 open parentheses 0 close parentheses close parentheses end cell row blank equals cell open parentheses 1 over 8 sin 120 degree minus 1 fourth sin 60 degree close parentheses minus open parentheses 1 over 8 sin 0 degree minus 1 fourth sin 0 degree close parentheses end cell row blank equals cell open parentheses 1 over 8.1 half square root of 3 minus 1 fourth.1 half square root of 3 close parentheses minus open parentheses 1 over 8 left parenthesis 0 right parenthesis minus 1 fourth left parenthesis 0 right parenthesis close parentheses end cell row blank equals cell 1 over 16 square root of 3 minus 1 over 8 square root of 3 end cell row blank equals cell 1 over 16 square root of 3 minus 2 over 16 square root of 3 end cell row blank equals cell negative 1 over 16 square root of 3 end cell end table end style

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