Pertanyaan

Hasil dari ∫ sin 4 x cos 4 x d x adalah ....

Hasil dari $\int sin^{4} x cos^{4} x d x$ adalah ....

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Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Ingat kembali rumus setengah sudut berikut ini. Maka,

Ingat kembali rumus setengah sudut berikut ini.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 2 A end cell equals cell 2 sin invisible function application A cos invisible function application blank A end cell row cell sin squared invisible function application A end cell equals cell fraction numerator 1 minus cos invisible function application 2 A over denominator 2 end fraction end cell row cell cos squared invisible function application A end cell equals cell fraction numerator cos invisible function application 2 A plus 1 over denominator 2 end fraction end cell end table end style$

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral sin to the power of 4 invisible function application x cos to the power of 4 invisible function application x d x end cell equals cell integral open parentheses sin invisible function application x cos invisible function application x close parentheses to the power of 4 d x end cell row blank equals cell integral open parentheses 1 half sin invisible function application 2 x close parentheses to the power of 4 d x end cell row blank equals cell 1 over 16 integral open parentheses sin squared invisible function application 2 x close parentheses squared d x end cell row blank equals cell 1 over 16 integral open parentheses fraction numerator 1 minus cos invisible function application 4 x over denominator 2 end fraction close parentheses squared d x end cell row blank equals cell 1 over 16 times 1 fourth integral open parentheses 1 minus 2 cos invisible function application 4 x plus cos squared invisible function application 4 x close parentheses d x end cell row blank equals cell 1 over 64 integral open parentheses 1 minus 2 cos invisible function application 4 x plus open parentheses fraction numerator cos invisible function application 8 x plus 1 over denominator 2 end fraction close parentheses close parentheses d x end cell row blank equals cell 1 over 64 integral open parentheses 1 minus 2 cos invisible function application 4 x plus 1 half cos invisible function application 8 x plus 1 half close parentheses d x end cell row blank equals cell 1 over 64 integral open parentheses 3 over 2 minus 2 cos invisible function application 4 x plus 1 half cos invisible function application 8 x close parentheses d x end cell row blank equals cell 1 over 64 integral open parentheses 3 over 2 minus 2 cos invisible function application 4 x plus 1 half cos invisible function application 8 x close parentheses d x end cell row blank equals cell 1 over 64 open parentheses 3 over 2 x minus 2 times 1 fourth sin invisible function application 4 x plus 1 half times 1 over 8 sin invisible function application 8 x close parentheses plus C end cell row blank equals cell 1 over 64 open parentheses 3 over 2 x minus 1 half sin invisible function application 4 x plus 1 over 16 sin invisible function application 8 x close parentheses plus C end cell row blank equals cell 1 over 128 open parentheses 3 x minus sin invisible function application 4 x plus 1 over 8 sin invisible function application 8 x close parentheses plus C end cell end table end style$