Pertanyaan

Tentukan hasil pengintegralanfungsi aljabar berikut. ∫ − 1 0 ( 2 − x 2 ) 2 x d x

Tentukan hasil pengintegralan fungsi aljabar berikut.

$\int_{- 1}^{0} \frac{x}{( 2 - x ^{2} ) ^{2}} d x$

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Misalkan , sehingga

Misalkan $begin mathsize 14px style u equals 2 minus x squared space maka space fraction numerator d u over denominator d x end fraction equals negative 2 x space atau space fraction numerator d u over denominator negative 2 x end fraction equals d x end style$ , sehingga

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