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Jika , hasil dari  adalah ...

Pertanyaan

Jika f open parentheses x close parentheses equals open parentheses x plus 3 close parentheses open parentheses 3 x minus 1 close parentheses, hasil dari integral f open parentheses x close parentheses space straight d x adalah ...

  1. x cubed minus 4 x squared minus 3 x plus C 

  2. x cubed plus 4 x squared minus 3 x plus C 

  3. x cubed plus 4 x squared plus 3 x plus C 

  4. x cubed minus 4 x squared plus 3 x plus C 

  5. 3 x cubed plus 4 x squared minus 3 x plus C 

Pembahasan Soal:

Konsep integral:

axndx=n+1axn+1+C,n=1,CR

Dengan menggunakan konsep integral maka hasil dari integral f open parentheses x close parentheses space straight d x adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell integral f open parentheses x close parentheses space straight d x end cell equals cell integral open parentheses x plus 3 close parentheses open parentheses 3 x minus 1 close parentheses space straight d x end cell row blank equals cell integral 3 x squared minus x plus 9 x minus 3 space straight d x end cell row blank equals cell integral 3 x squared plus 8 x minus 3 space straight d x end cell row blank equals cell fraction numerator 3 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus fraction numerator 8 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 3 x plus C end cell row blank equals cell 3 over 3 x cubed plus 8 over 2 x squared minus 3 x plus C end cell row blank equals cell x cubed plus 4 x squared minus 3 x plus C end cell end table 

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

O. Rahmawati

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Terakhir diupdate 30 Agustus 2021

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Pertanyaan yang serupa

Selesaikanlah integral berikut! a.

Pembahasan Soal:

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral x open parentheses square root of x minus 1 close parentheses space straight d x end cell equals cell space integral x open parentheses x to the power of 1 half end exponent minus 1 close parentheses space straight d x end cell row blank equals cell space integral x to the power of 3 over 2 end exponent minus x space straight d x end cell row blank equals cell fraction numerator 1 over denominator begin display style 5 over 2 end style end fraction x to the power of 5 over 2 end exponent minus 1 half x squared plus C end cell row blank equals cell 2 over 5 x to the power of 5 over 2 end exponent minus 1 half x squared plus C end cell row blank equals cell 2 over 5 x squared square root of x minus 1 half x squared plus C end cell end table 

Jadi, Error converting from MathML to accessible text..

1

Roboguru

Hitunglah hasil dari !

Pembahasan Soal:

Diperoleh hasil integralnya yaitu:

begin mathsize 12px style integral open parentheses 2 x minus 2 close parentheses open parentheses 3 minus 2 x close parentheses cubed space d x equals integral open parentheses 2 x minus 2 close parentheses open parentheses 27 minus 54 x plus 36 x squared minus 8 x cubed close parentheses space d x equals integral 54 x minus 108 x squared plus 72 x cubed minus 16 x to the power of 4 minus 54 plus 108 x minus 72 x squared plus 16 x cubed space d x equals integral negative 16 x to the power of 4 plus 88 x cubed minus 180 x squared plus 162 x minus 54 space d x equals negative 16 over 5 x to the power of 5 plus 22 x to the power of 4 minus 60 x cubed plus 81 x squared minus 54 x plus straight C end style

Maka, hasil dari integral open parentheses 2 x minus 2 close parentheses open parentheses 3 minus 2 x close parentheses cubed space d x adalah Error converting from MathML to accessible text..

0

Roboguru

Nilai

Pembahasan Soal:

Nilai integral tersebut adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral square root of x open parentheses 3 over 2 cube root of x plus 3 close parentheses space d x end cell row blank equals cell integral x to the power of 1 half end exponent open parentheses 3 over 2 x to the power of 1 third end exponent plus 3 close parentheses d x end cell row blank equals cell integral open parentheses 3 over 2 x to the power of 1 half plus 1 third end exponent plus 3 x to the power of 1 half end exponent close parentheses d x end cell row blank equals cell integral open parentheses 3 over 2 x to the power of 5 over 6 end exponent plus 3 x to the power of 1 half end exponent close parentheses d x end cell row blank equals cell 3 over 2 times 6 over 11 x to the power of 11 over 6 end exponent plus 3 times 2 over 3 x to the power of 3 over 2 end exponent plus c end cell row blank equals cell 9 over 11 x root index 6 of x to the power of 5 end root plus 2 x square root of x plus c end cell end table

Dengan demikian, nilai integral square root of x open parentheses 3 over 2 cube root of x plus 3 close parentheses space d x equals 9 over 11 x root index 6 of x to the power of 5 end root plus 2 x square root of x plus c 

0

Roboguru

Selesaikanlah integral berikut! f.

Pembahasan Soal:

Perhatikan perhitungan berikut.

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

Jadi, Error converting from MathML to accessible text..

1

Roboguru

Hasil dari

Pembahasan Soal:

integral left parenthesis 2 x plus 3 right parenthesis left parenthesis x minus 4 right parenthesis d x equals integral left parenthesis 2 x squared minus 5 x minus 12 right parenthesis d x  equals 2 over 3 x cubed minus 5 over 2 x squared minus 12 x plus C

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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