Pertanyaan

Hasil dari adalah ....

Hasil dari $begin mathsize 14px style integral fraction numerator open parentheses x minus 1 close parentheses squared open parentheses x squared minus 2 close parentheses over denominator x minus square root of 2 end fraction blank d x end style$ adalah ....

$begin mathsize 14px style 1 fourth x to the power of 4 plus fraction numerator square root of 2 minus 2 over denominator 3 end fraction x cubed minus fraction numerator 2 square root of 2 plus 1 over denominator 2 end fraction x squared plus square root of 2 x plus C end style$
$begin mathsize 14px style 1 fourth x to the power of 4 plus fraction numerator square root of 2 minus 2 over denominator 3 end fraction x cubed plus fraction numerator square root of 2 plus 1 over denominator 2 end fraction x squared minus square root of 2 x plus C end style$
$begin mathsize 14px style 1 fourth x to the power of 4 plus fraction numerator square root of 2 minus 2 over denominator 3 end fraction x cubed minus fraction numerator square root of 2 plus 1 over denominator 2 end fraction 2 x squared minus square root of 2 x plus C end style$

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan perhitungan berikut ini! Jika dimisalkan maka Jadi, jawaban yang tepat adalah A.

Perhatikan perhitungan berikut ini!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator left parenthesis x minus 1 right parenthesis squared left parenthesis x to the power of 2 end exponent minus 2 right parenthesis over denominator x minus square root of 2 end fraction space d x end cell equals cell integral fraction numerator left parenthesis x minus 1 right parenthesis squared left parenthesis x plus square root of 2 right parenthesis left parenthesis x minus square root of 2 right parenthesis over denominator x minus square root of 2 end fraction space d x end cell row blank equals cell integral left parenthesis x minus 1 right parenthesis squared left parenthesis x plus square root of 2 right parenthesis space d x end cell row blank equals cell integral left parenthesis x squared minus 2 x plus 1 right parenthesis left parenthesis x plus square root of 2 right parenthesis space d x end cell row blank equals cell integral left parenthesis x cubed plus square root of 2 x squared minus 2 x squared minus 2 square root of 2 x plus x plus square root of 2 right parenthesis space d x end cell row blank equals cell integral left parenthesis x cubed plus left parenthesis square root of 2 minus 2 right parenthesis x squared minus open parentheses 2 square root of 2 plus 1 close parentheses x plus square root of 2 right parenthesis space d x end cell row blank equals cell open parentheses fraction numerator 1 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent plus C subscript 1 close parentheses plus left parenthesis square root of 2 minus 2 right parenthesis open parentheses fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus C subscript 2 close parentheses minus open parentheses 2 square root of 2 plus 1 close parentheses open parentheses fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus C subscript 3 close parentheses plus square root of 2 open parentheses x plus C subscript 4 close parentheses end cell row blank equals cell 1 fourth x to the power of 4 plus fraction numerator square root of 2 minus 1 over denominator 3 end fraction x cubed minus fraction numerator 2 square root of 2 plus 1 over denominator 2 end fraction x squared plus square root of 2 x plus C subscript 1 plus left parenthesis square root of 2 minus 2 right parenthesis C subscript 2 minus open parentheses 2 square root of 2 plus 1 close parentheses C subscript 3 plus square root of 2 C subscript 4 end cell end table end style$

Jika dimisalkan maka

$size 14px 1 over size 14px 4 size 14px x to the power of size 14px 4 size 14px plus fraction numerator square root of size 14px 2 size 14px minus size 14px 1 over denominator size 14px 3 end fraction size 14px x to the power of size 14px 3 size 14px minus fraction numerator size 14px 2 square root of size 14px 2 size 14px plus size 14px 1 over denominator size 14px 2 end fraction size 14px x to the power of size 14px 2 size 14px plus square root of size 14px 2 size 14px x size 14px plus size 14px C subscript size 14px 1 size 14px plus size 14px left parenthesis square root of size 14px 2 size 14px minus size 14px 2 size 14px right parenthesis size 14px C subscript size 14px 2 size 14px minus begin mathsize 14px style left parenthesis 2 square root of 2 plus 1 right parenthesis end style size 14px C subscript size 14px 3 size 14px plus square root of size 14px 2 size 14px C subscript size 14px 4 size 14px equals size 14px 1 over size 14px 4 size 14px x to the power of size 14px 4 size 14px plus fraction numerator square root of size 14px 2 size 14px minus size 14px 1 over denominator size 14px 3 end fraction size 14px x to the power of size 14px 3 size 14px minus fraction numerator size 14px 2 square root of size 14px 2 size 14px plus size 14px 1 over denominator size 14px 2 end fraction size 14px x to the power of size 14px 2 size 14px plus square root of size 14px 2 size 14px x size 14px plus size 14px C$

Jadi, jawaban yang tepat adalah A.