Roboguru

Pertanyaan

Hasil dari integral fraction numerator 9 x squared minus 60 x plus 12 over denominator square root of x cubed minus 10 x squared plus 4 x minus 7 end root end fraction blank straight d x adalah ….

  1. negative 6 square root of x cubed minus 10 x squared plus 4 x minus 7 end root plus C  

  2. negative 3 square root of x cubed minus 10 x squared plus 4 x minus 7 end root plus C  

  3. negative 2 square root of x cubed minus 10 x squared plus 4 x minus 7 end root plus C  

  4. 3 square root of x cubed minus 10 x squared plus 4 x minus 7 end root plus C  

  5. 6 square root of x cubed minus 10 x squared plus 4 x minus 7 end root plus C  

M. Haidar.

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Dari soal diberikan integral aljabar sebagai berikut.

integral fraction numerator 9 x squared minus 60 x plus 12 over denominator square root of x cubed minus 10 x squared plus 4 x minus 7 end root end fraction blank straight d x

 

Jika x cubed minus 10 x squared plus 4 x minus 7 equals u, maka didapat perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals cell 3 x squared minus 20 x plus 4 end cell row cell integral open parentheses fraction numerator straight d u over denominator straight d x end fraction close parentheses straight d x end cell equals cell integral open parentheses 3 x squared minus 20 x plus 4 close parentheses straight d x end cell row cell integral straight d u end cell equals cell integral open parentheses 3 x squared minus 20 x plus 4 close parentheses straight d x end cell end table  

Kemudian, perhatikan bahwa

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral fraction numerator 9 x squared minus 60 x plus 12 over denominator square root of x cubed minus 10 x squared plus 4 x minus 7 end root end fraction blank straight d x end cell row blank equals cell integral fraction numerator 3 open parentheses 3 x squared minus 20 x plus 4 close parentheses over denominator square root of x cubed minus 10 x squared plus 4 x minus 7 end root end fraction blank straight d x end cell row blank equals cell 3 integral fraction numerator 1 over denominator square root of u end fraction blank straight d u end cell row blank equals cell 3 integral u to the power of negative 1 half end exponent blank straight d u end cell row blank equals cell 3 times 2 u to the power of 1 half end exponent plus straight C end cell row blank equals cell 6 square root of u plus straight C end cell end table   

Ingat kembali bahwa u equals x cubed minus 10 x squared plus 4 x minus 7 sehingga diperoleh hasil sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 9 x squared minus 60 x plus 12 over denominator square root of x cubed minus 10 x squared plus 4 x minus 7 end root end fraction blank straight d x end cell equals cell 6 square root of u plus C end cell row blank equals cell 6 square root of x cubed minus 10 x squared plus 4 x minus 7 end root plus C end cell end table

Jadi, jawaban yang tepat adalah E.

31

0.0 (0 rating)

Pertanyaan serupa

Hasil dari  adalah ….

44

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia