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Pertanyaan

integral x open parentheses x minus 6 close parentheses squared d x equals....

  1. x cubed minus 12 x squared plus 36 x plus text C  end text

  2. 1 fourth x to the power of 4 minus 18 x squared plus text C  end text

  3. 1 fourth x to the power of 4 minus 3 x cubed plus 18 x squared plus text C  end text

  4. 1 fourth x to the power of 4 minus 4 x cubed plus 18 x squared plus text C  end text

  5. 1 fourth x to the power of 4 minus 4 x cubed minus 18 x squared plus text C  end text

Pembahasan Soal:

nilai integral x open parentheses x minus 6 close parentheses squared d x dapat ditentukan menggunakan cara parsial yaitu integral u d v equals u v minus integral v d u dengan u equals x space text dan end text space d v equals open parentheses x minus 6 close parentheses squared d x comma maka

u space space equals x space space space space space space space text dan end text space d v equals open parentheses x minus 6 close parentheses squared d x d u equals 1 d x space space space space space space space space space space space space v equals integral open parentheses x minus 6 close parentheses squared d x d u equals d x space space space space space space space space space space space space space space v equals integral open parentheses x minus 6 close parentheses squared d open parentheses x minus 6 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space v equals open parentheses x minus 6 close parentheses cubed over 3 plus text C end text

Nilai integral x open parentheses x minus 6 close parentheses squared d x adalah

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral u d v end cell equals cell u v minus integral v d u end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell open parentheses x cross times open parentheses x minus 6 close parentheses cubed over 3 close parentheses minus integral open parentheses x minus 6 close parentheses cubed over 3 d x end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell fraction numerator x open parentheses x minus 6 close parentheses cubed over denominator 3 end fraction minus 1 third integral open parentheses x minus 6 close parentheses cubed d open parentheses x minus 6 close parentheses end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell fraction numerator x open parentheses x minus 6 close parentheses cubed over denominator 3 end fraction minus 1 third open parentheses x minus 6 close parentheses to the power of 4 over 4 plus text C end text end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell open parentheses x minus 6 close parentheses squared over 3 open parentheses x open parentheses x minus 6 close parentheses minus 1 fourth open parentheses x minus 6 close parentheses squared close parentheses plus text C end text end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell fraction numerator x squared minus 12 x plus 36 over denominator 3 end fraction open parentheses x squared minus 6 x minus 1 fourth open parentheses x squared minus 12 x plus 36 close parentheses close parentheses plus text C end text end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell fraction numerator x squared minus 12 x plus 36 over denominator 3 end fraction open parentheses fraction numerator 4 x squared minus 24 x minus x squared plus 12 x minus 36 over denominator 4 end fraction close parentheses plus text C end text end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell fraction numerator x squared minus 12 x plus 36 over denominator up diagonal strike 3 end fraction open parentheses fraction numerator up diagonal strike 3 x squared begin display style stack up diagonal strike negative 12 end strike with 4 on top end style x begin display style stack up diagonal strike negative 36 end strike with 12 on top end style over denominator 4 end fraction close parentheses plus text C end text end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell fraction numerator open parentheses x squared minus 12 x plus 36 close parentheses open parentheses x squared minus 4 x minus 12 close parentheses over denominator 4 end fraction plus text C end text end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell fraction numerator x to the power of 4 minus 16 x cubed plus 72 x squared minus 432 over denominator 4 end fraction plus text C end text end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell 1 fourth x to the power of 4 minus 4 x cubed plus 18 x squared minus 108 plus text C end text end cell row cell integral x open parentheses x minus 6 close parentheses squared d x end cell equals cell 1 fourth x to the power of 4 minus 4 x cubed plus 18 x squared plus text C end text end cell end table end style


Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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