Pertanyaan

∫ sin 3 x d x adalah...

$\int sin^{3} x d x$ adalah...

$fraction numerator negative cos space x space sin squared x over denominator 3 end fraction plus 2 over 3 left parenthesis cos space x right parenthesis plus C$
$fraction numerator cos space x space sin squared x over denominator 3 end fraction minus 4 over 3 left parenthesis cos space x right parenthesis plus C$
$fraction numerator negative tan space x space sin squared x over denominator 2 end fraction minus 2 over 3 left parenthesis cosec space x right parenthesis plus C$
$fraction numerator negative cos space x space sin squared x over denominator 3 end fraction minus 2 over 3 left parenthesis cos space x right parenthesis plus C$
$fraction numerator cos space x space sin squared x over denominator 3 end fraction plus 1 half left parenthesis cosec space x right parenthesis plus C$

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Pembahasan

Cara -1 Ingat bahwa Gunakan integral substitusi misalkan sehingga bentuk integral menjadi Cara-2 Pilih maka Sehingga,

Cara -1

Ingat bahwa

integral sin space x. open parentheses 1 minus cos squared space x close parentheses d x integral sin space x space d x minus integral sin space x. space cos squared space x space d x minus cos space x minus integral sin space x. space cos squared space x space d x

Gunakan integral substitusi misalkan

$fraction numerator d u over denominator d x end fraction equals negative sin space x space left right double arrow space d x equals negative fraction numerator d u over denominator sin begin display style space end style begin display style x end style end fraction comma$ sehingga bentuk integral menjadi

$negative cos space x minus integral sin space x. u squared fraction numerator d u over denominator negative sin x end fraction equals negative cos space x plus integral u squared space d u equals negative cos space x plus 1 third u cubed plus C equals negative cos space x plus 1 third cos cubed space x plus C$

Cara-2

Pilih

maka

Sehingga,

$integral sin cubed space x space d x equals integral sin squared space x space d open parentheses negative cos space x close parentheses space space space space space space space space space space space space space space space space space space space space equals negative cos space x space sin squared space x minus integral negative cos space x space d open parentheses sin squared space x close parentheses d x space space space space space space space space space space space space space space space space space space space space equals negative cos space x space si n squared space x plus integral cos space x space 2 space sin space x space cos space x space d x space space space space space space space space space space space space space space space space space space space space equals negative cos space x space sin squared space x plus 2 integral sin space x space open parentheses 1 minus sin squared space x close parentheses space d x integral sin cubed space x space d x equals negative cos space x space sin squared space x plus 2 space integral sin space x space d x space minus space 2 space integral sin cubed space d x left right arrow 3 integral sin cubed space x space d x equals negative cos space x space sin squared space x plus 2 space integral sin space x space d x space left right arrow integral sin cubed space x space d x equals fraction numerator negative cos space x space sin squared space x over denominator 3 end fraction plus 2 over 3 integral sin space x space d x space equals fraction numerator negative cos space x space sin squared space x over denominator 3 end fraction plus 2 over 3 open parentheses cos space x close parentheses plus C$