Roboguru

Hasil dari  adalah ....

Pertanyaan

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 ....

  1. 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 

  2. 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 

  3. 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 

  4. begin mathsize 14px style 1 fourth x to the power of 4 minus 4 over 3 x cubed plus 5 over 2 x squared minus 2 x plus C end style 

  5. begin mathsize 14px style 1 third x cubed minus x squared plus x plus C end style 

Pembahasan Soal:

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 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell C subscript 1 plus left parenthesis square root of 2 minus 2 right parenthesis C subscript 2 minus left parenthesis 2 square root of 2 plus 1 right parenthesis C subscript 3 plus square root of 2 C subscript 4 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table end style 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.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLSATU

Terakhir diupdate 13 Desember 2020

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