Pertanyaan

Hasil dari ∫ 16 − 9 x 2 d x = ....

Hasil dari $\int \frac{d x}{16 - 9 x ^{2}} =$ ....

$begin mathsize 14px style 3 open parentheses a r c sin invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$
$begin mathsize 14px style 3 open parentheses a r c sec invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$
$begin mathsize 14px style 3 open parentheses a r c tan invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$
$begin mathsize 14px style 1 third open parentheses a r c sin invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$
$begin mathsize 14px style 1 third open parentheses a r c sec invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Misalkan: Ingat juga rumus identitas trigonometri : Maka,

Misalkan:

$begin mathsize 14px style x equals 4 over 3 sin invisible function application a a equals a r c sin invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses d x equals 4 over 3 space cos invisible function application a d a end style$

Ingat juga rumus identitas trigonometri :

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator d x over denominator square root of 16 minus 9 x squared end root end fraction end cell equals cell integral fraction numerator 4 over 3 space cos invisible function application a over denominator square root of 16 minus 9 open parentheses 4 over 3 sin invisible function application a close parentheses squared end root end fraction d a end cell row blank equals cell integral fraction numerator 4 over 3 space cos invisible function application a over denominator square root of 16 minus 9 open parentheses 16 over 9 sin squared invisible function application a close parentheses end root end fraction d a end cell row blank equals cell integral fraction numerator 4 over 3 space cos invisible function application a over denominator square root of 16 minus 16 sin squared invisible function application a end root end fraction d a end cell row blank equals cell integral fraction numerator 4 over 3 space cos invisible function application a over denominator square root of 16 open parentheses 1 minus sin squared invisible function application a close parentheses end root end fraction d a end cell row blank equals cell integral fraction numerator 4 over 3 space cos invisible function application a over denominator square root of 16 cos squared invisible function application a end root end fraction d a end cell row blank equals cell integral fraction numerator 4 over 3 space cos invisible function application a over denominator 4 cos invisible function application a end fraction d a end cell row blank equals cell integral 1 third d a end cell row blank equals cell 1 third a plus C end cell row blank equals cell 1 third open parentheses a r c sin invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end cell end table end style$