Pertanyaan

Hasil dari ∫ 16 − 9 x 2 d x = ....

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

$begin mathsize 14px style 8 over 3 open parentheses 3 x square root of 16 minus 9 x squared end root plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$
$begin mathsize 14px style 4 over 3 open parentheses 3 x square root of 16 minus 9 x squared end root plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$
$begin mathsize 14px style 2 over 3 open parentheses 3 x square root of 16 minus 9 x squared end root plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$
$begin mathsize 14px style 2 over 3 open parentheses 4 x square root of 16 minus 9 x squared end root plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$
$begin mathsize 14px style 4 over 3 open parentheses 4 x square root of 16 minus 9 x squared end root plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end style$

8 dari 10 siswa nilainya naik

dengan paket belajar pilihan

Habis dalam

Klaim

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Misalkan: Sehingga diperoleh 4 adalah sisi miring sebuah segitiga siku-siku dengan kedua sisi tegaknya dan . Maka diperoleh dan Jika kita integralkan kedua ruas maka diperoleh Sehingga, Jadi, jawaban yang tepat adalah C.

Misalkan:

Sehingga diperoleh 4 adalah sisi miring sebuah segitiga siku-siku dengan kedua sisi tegaknya dan .

Maka diperoleh

$begin mathsize 14px style cos invisible function application theta equals fraction numerator square root of 16 minus 9 x squared end root over denominator 4 end fraction end style$

dan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application theta end cell equals cell fraction numerator 3 x over denominator 4 end fraction rightwards arrow theta equals sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses end cell row x equals cell 4 over 3 sin invisible function application theta end cell row cell fraction numerator d x over denominator d theta end fraction end cell equals cell 4 over 3 cos invisible function application theta end cell end table end style$

Jika kita integralkan kedua ruas maka diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator d x over denominator d theta end fraction d theta end cell equals cell 4 over 3 integral cos invisible function application theta d theta end cell row cell integral d x end cell equals cell 4 over 3 integral cos invisible function application theta d theta end cell end table end style$

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral square root of 16 minus 9 x squared end root blank d x end cell equals cell 4 over 3 integral square root of 16 minus 9 open parentheses 4 over 3 sin invisible function application theta close parentheses squared end root times cos invisible function application theta d theta end cell row blank equals cell 4 over 3 integral square root of 16 minus 16 sin squared invisible function application theta end root times cos invisible function application theta d theta end cell row blank equals cell 4 over 3 integral square root of 16 open parentheses 1 minus sin squared invisible function application theta close parentheses end root times cos invisible function application theta d theta end cell row blank equals cell 4 over 3 integral square root of 16 cos squared invisible function application theta end root times cos invisible function application theta d theta end cell row blank equals cell 4 over 3 integral 4 cos squared invisible function application theta d theta end cell row blank equals cell 16 over 3 integral fraction numerator cos invisible function application 2 theta plus 1 over denominator 2 end fraction d theta end cell row blank equals cell 8 over 3 integral open parentheses cos invisible function application 2 theta plus 1 close parentheses d theta end cell row blank equals cell 8 over 3 open parentheses 1 half sin invisible function application 2 theta plus theta close parentheses plus C end cell row blank equals cell 8 over 3 open parentheses 1 half times 2 sin invisible function application theta cos invisible function application theta plus theta close parentheses plus C end cell row blank equals cell 8 over 3 open parentheses fraction numerator 3 x over denominator 4 end fraction times fraction numerator square root of 16 minus 9 x squared end root over denominator 4 end fraction plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses close parentheses plus C end cell row blank equals cell 2 over 3 open parentheses 3 x square root of 16 minus 9 x squared end root plus sin to the power of negative 1 end exponent 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$

Jadi, jawaban yang tepat adalah C.