Pertanyaan

Hasil dari ∫ 3 x 2 − 4 1 d x = ....

Hasil dari $\int \frac{1}{3 x ^{2} - 4} d x =$ ....

$begin mathsize 14px style fraction numerator 2 over denominator square root of 3 end fraction ln invisible function application open vertical bar fraction numerator square root of 3 x over denominator 2 end fraction plus fraction numerator square root of 3 x squared minus 4 end root over denominator 2 end fraction close vertical bar plus C end style$
$begin mathsize 14px style fraction numerator 1 over denominator square root of 3 end fraction ln invisible function application open vertical bar fraction numerator square root of 3 x over denominator 2 end fraction plus fraction numerator square root of 3 x squared minus 4 end root over denominator 2 end fraction close vertical bar plus C end style$
$begin mathsize 14px style square root of 3 ln invisible function application open vertical bar fraction numerator square root of 3 x over denominator 2 end fraction plus fraction numerator square root of 3 x squared minus 4 end root over denominator 2 end fraction close vertical bar plus C end style$
$begin mathsize 14px style fraction numerator 1 over denominator 2 square root of 3 end fraction ln invisible function application open vertical bar fraction numerator square root of 3 x over denominator 2 end fraction plus fraction numerator square root of 3 x squared minus 4 end root over denominator 2 end fraction close vertical bar plus C end style$
$begin mathsize 14px style 2 square root of 3 ln invisible function application open vertical bar fraction numerator square root of 3 x over denominator 2 end fraction plus fraction numerator square root of 3 x squared minus 4 end root over denominator 2 end fraction close vertical bar plus C end style$

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Misalkan: Sehingga diperoleh adalah sisi miring sebuah segitiga siku-siku dengan kedua sisi tegaknya dan 2. Maka diperoleh dan Jika kita integralkan kedua ruas maka diperoleh Sehingga, Kemudian ingat kembali integral berikut ini pada pembahasan sebelumnya. Sehingga, Jadi, jawaban yang tepat adalah B.

Misalkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell square root of 3 x squared minus 4 end root end cell row cell y squared end cell equals cell 3 x squared minus 2 squared end cell row cell y squared plus 2 squared end cell equals cell open parentheses square root of 3 x close parentheses squared end cell end table end style

Sehingga diperoleh adalah sisi miring sebuah segitiga siku-siku dengan kedua sisi tegaknya dan 2.

Maka diperoleh

$begin mathsize 14px style tan invisible function application theta equals y over 2 equals fraction numerator square root of 3 x squared minus 4 end root over denominator 2 end fraction end style$

dan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sec invisible function application theta end cell equals cell fraction numerator square root of 3 x over denominator 2 end fraction end cell row x equals cell fraction numerator 2 over denominator square root of 3 end fraction space sec invisible function application theta end cell row cell fraction numerator d x over denominator d theta end fraction end cell equals cell fraction numerator 2 over denominator square root of 3 end fraction sec invisible function application theta tan invisible function application theta end cell end table end style$

Jika kita integralkan kedua ruas maka diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator d x over denominator d theta end fraction d theta end cell equals cell fraction numerator 2 over denominator square root of 3 end fraction integral sec invisible function application theta tan invisible function application theta d theta end cell row cell integral d x end cell equals cell fraction numerator 2 over denominator square root of 3 end fraction integral sec invisible function application theta tan invisible function application theta d theta end cell end table end style$

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 1 over denominator square root of 3 x squared minus 4 end root end fraction blank d x end cell equals cell fraction numerator 2 over denominator square root of 3 end fraction integral fraction numerator 1 over denominator square root of 3 open parentheses fraction numerator 2 over denominator square root of 3 end fraction space sec invisible function application theta close parentheses squared minus 4 end root end fraction times sec invisible function application theta tan invisible function application theta d theta end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction integral fraction numerator 1 over denominator square root of 4 sec squared invisible function application theta minus 4 end root end fraction times sec invisible function application theta tan invisible function application theta d theta end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction integral fraction numerator 1 over denominator square root of 4 open parentheses sec squared invisible function application theta minus 1 close parentheses end root end fraction times sec invisible function application theta tan invisible function application theta d theta end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction integral fraction numerator 1 over denominator square root of 4 tan squared invisible function application theta end root end fraction times sec invisible function application theta tan invisible function application theta d theta end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction integral fraction numerator 1 over denominator 2 tan invisible function application theta end fraction times sec invisible function application theta tan invisible function application theta d theta end cell row blank equals cell fraction numerator 1 over denominator square root of 3 end fraction integral sec invisible function application theta d theta end cell end table end style$

Kemudian ingat kembali integral berikut ini pada pembahasan sebelumnya.

Sehingga,

Jadi, jawaban yang tepat adalah B.