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Pertanyaan

Hasil dari ∫ 2 x ⋅ e 6 x dx = … + 3 m u .

Hasil dari    

  1. begin mathsize 14px style straight e to the power of 6 straight x end exponent over 9 left parenthesis 6 straight x minus 1 right parenthesis plus straight C end style  

  2. begin mathsize 14px style straight e to the power of 6 straight x end exponent over 18 left parenthesis 6 straight x minus 1 right parenthesis plus straight C end style   

  3. begin mathsize 14px style straight e to the power of 6 straight x end exponent over 9 left parenthesis 3 straight x minus 1 right parenthesis plus straight C end style  

  4. begin mathsize 14px style straight e to the power of 6 straight x end exponent over 3 left parenthesis 6 straight x minus 1 right parenthesis plus straight C end style   

  5. begin mathsize 14px style straight e to the power of 6 straight x end exponent over 3 left parenthesis 3 straight x minus 1 right parenthesis plus straight C end style   

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

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Pembahasan

Ingat kembali bahwa integral parsial berikut ini. Perhatikan bentuk integral berikut ini! Misalkan: u = 2x du = 2 dx Dan Sehingga Jadi, jawaban yang benar adalah B.

Ingat kembali bahwa integral parsial berikut ini.

begin mathsize 14px style integral straight u space dv equals uv minus integral straight v space du integral straight e to the power of ax space dx equals 1 over straight a straight e to the power of ax plus straight C end style   

Perhatikan bentuk integral berikut ini!

begin mathsize 14px style integral 2 straight x times straight e to the power of 6 straight x end exponent space dx end style  

Misalkan:
u = 2x
du = 2 dx

Dan

begin mathsize 14px style dv equals straight e to the power of 6 straight x end exponent space dx integral dv equals integral straight e to the power of 6 straight x end exponent space dx straight v equals 1 over 6 straight e to the power of 6 straight x end exponent end style

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral 2 straight x times straight e to the power of 6 straight x end exponent space dx end cell equals cell 2 straight x times 1 over 6 straight e to the power of 6 straight x end exponent minus integral 1 over 6 straight e to the power of 6 straight x end exponent times 2 space dx end cell row blank equals cell 1 third xe to the power of 6 straight x end exponent minus 1 third integral straight e to the power of 6 straight x end exponent plus straight C end cell row blank equals cell 1 third xe to the power of 6 straight x end exponent minus 1 third open parentheses 1 over 6 straight e to the power of 6 straight x end exponent close parentheses plus straight C end cell row blank equals cell straight e to the power of 6 straight x end exponent over 18 left parenthesis 6 straight x minus 1 right parenthesis plus straight C end cell end table end style    

Jadi, jawaban yang benar adalah B. 

 

 

 

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