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Pertanyaan

8 1 ​ ∫ 3 1 ​ ​ x 2 3 ​ 1 + x 1 ​ ​ dx = ....

....

  1. 19

  2. 38

  3. 57

  4. 76

  5. 95

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R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

jawaban yang tepat adalah B.

Pembahasan

Misalkan , maka Sehingga Jadi, jawaban yang tepat adalah B.

Misalkan begin mathsize 14px style u equals 1 plus 1 over x end style, maka

begin mathsize 14px style du over dx equals minus sign 1 over x squared du equals minus sign 1 over x squared dx x equals 1 over 8 yields u equals 1 plus fraction numerator 1 over denominator 1 over 8 end fraction equals 1 plus 8 equals 9 x equals 1 third yields u equals 1 plus fraction numerator 1 over denominator 1 third end fraction equals 1 plus 3 equals 4 end style  
 

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral with 1 over 8 below and 1 third on top 3 over x squared square root of 1 plus 1 over x end root dx end cell equals cell negative sign 3 integral with 1 over 8 below and 1 third on top square root of 1 plus 1 over x end root middle dot open parentheses negative sign 1 over x squared close parentheses dx end cell row blank equals cell negative sign 3 integral with 9 below and 4 on top square root of u du end cell row blank equals cell negative sign 3 integral with 9 below and 4 on top u to the power of 1 half end exponent du end cell row blank equals cell negative sign 3 middle dot 2 over 3 open parentheses u to the power of 3 over 2 end exponent close parentheses open vertical bar 4 over 9 close end cell row blank equals cell negative sign 2 open parentheses 4 to the power of 3 over 2 end exponent close parentheses minus sign open parentheses negative sign 2 open parentheses 9 to the power of 3 over 2 end exponent close parentheses close parentheses end cell row blank equals cell negative sign 2 open parentheses open parentheses 2 squared close parentheses to the power of 3 over 2 end exponent close parentheses plus 2 open parentheses open parentheses 3 squared close parentheses to the power of 3 over 2 end exponent close parentheses end cell row blank equals cell negative sign 2 open parentheses 2 cubed close parentheses plus 2 open parentheses 3 cubed close parentheses end cell row blank equals cell negative sign 2 open parentheses 8 close parentheses plus 2 open parentheses 27 close parentheses end cell row blank equals cell negative sign 16 plus 54 end cell row blank equals 38 end table end style  

Jadi, jawaban yang tepat adalah B.

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