Pertanyaan

Hasil dari ∫ 2 3 x 2 − x − 2 2 x − 1 d x adalah....

Hasil dari $\int_{2}^{3} \frac{2 x - 1}{x ^{2} - x - 2} d x$ adalah....

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Misalkan . Perhatikan Jadi, jawaban yang tepat adalah A.

Misalkan $begin mathsize 14px style u equals x squared minus x minus 2 space mak a space fraction numerator d u over denominator d x end fraction equals 2 x minus 1 space atau space fraction numerator d u over denominator 2 x minus 1 end fraction equals d x end style$ .

Perhatikan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 2 superscript 3 fraction numerator 2 x minus 1 over denominator square root of x squared minus x minus 2 end root end fraction d x end cell equals cell integral subscript 2 superscript 3 fraction numerator 2 x minus 1 over denominator open parentheses u close parentheses to the power of begin display style 1 half end style end exponent end fraction fraction numerator d u over denominator 2 x minus 1 end fraction end cell row blank equals cell integral subscript 2 superscript 3 u to the power of negative 1 half end exponent d u end cell row blank equals cell 2 open square brackets square root of u close square brackets subscript 2 superscript 3 end cell row blank equals cell 2 open square brackets square root of x squared minus x minus 2 end root close square brackets subscript 2 superscript 3 end cell row blank equals cell 2 open square brackets open parentheses 2 minus 0 close parentheses close square brackets end cell row blank equals 4 end table end style$

Jadi, jawaban yang tepat adalah A.