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Hasil dari  = ....

Pertanyaan

Hasil dari integral fraction numerator 3 x minus 1 over denominator open parentheses 3 x squared minus 2 x plus 7 close parentheses to the power of 7 end fraction d x = .... 

  1. negative fraction numerator 1 over denominator 3 left parenthesis 3 x squared minus 2 x plus 7 right parenthesis to the power of 6 end fraction plus straight C 

  2. negative fraction numerator 1 over denominator 4 left parenthesis 3 x squared minus 2 x plus 7 right parenthesis to the power of 6 end fraction plus straight C 

  3. negative fraction numerator 1 over denominator 6 left parenthesis 3 x squared minus 2 x plus 7 right parenthesis to the power of 6 end fraction plus straight C 

  4. negative fraction numerator 1 over denominator 12 left parenthesis 3 x squared minus 2 x plus 7 right parenthesis to the power of 6 end fraction plus straight C 

  5. negative fraction numerator 1 over denominator 12 left parenthesis 3 x squared minus 2 x plus 7 right parenthesis to the power of 7 end fraction plus straight C 

Pembahasan Soal:

Diketahuiintegral fraction numerator 3 x minus 1 over denominator open parentheses 3 x squared minus 2 x plus 7 close parentheses to the power of 7 end fraction straight d x

Ditanya hasil dari intergal tersebut ?

Dengan menggunakan konsep integral tak tentu.

Misal: 

straight u equals 3 x squared minus 2 x plus 7
table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d u over denominator d x end fraction end cell equals cell 6 x minus 2 end cell row cell d x end cell equals cell fraction numerator d u over denominator 6 x minus 2 end fraction end cell end table
du equals open parentheses 6 x minus 2 close parentheses straight d x

Maka, 

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

Dengan demikian, hasil dari integral fraction numerator 3 x minus 1 over denominator open parentheses 3 x squared minus 2 x plus 7 close parentheses to the power of 7 end fraction straight d x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 12 left parenthesis 3 x squared minus 2 x plus 7 right parenthesis to the power of 6 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight C end table

Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

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