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Hasil dari ∫02​3(x+1)(x−6)dx=....

Pertanyaan

Hasil dari integral subscript 0 superscript 2 3 open parentheses x plus 1 close parentheses open parentheses x minus 6 close parentheses d x equals.... 

  1. negative 14 

  2. negative 56 

  3. negative 28 

  4. negative 58 

  5. negative 16 

K. Prameswari

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.space  

Pembahasan

Ingat bahwa

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b f left parenthesis x right parenthesis d x end cell equals cell F left parenthesis b right parenthesis minus F left parenthesis a right parenthesis end cell row cell integral subscript a superscript b k f left parenthesis x right parenthesis d x end cell equals cell k integral subscript a superscript b f left parenthesis x right parenthesis d x comma space untuk space k space suatu space konstanta end cell end table 

Sehingga dapat diperoleh

begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 0 superscript 2 3 open parentheses x plus 1 close parentheses open parentheses x minus 6 close parentheses d x end cell row blank equals cell 3 integral subscript 0 superscript 2 open parentheses x plus 1 close parentheses open parentheses x minus 6 close parentheses d x end cell row blank equals cell 3 integral subscript 0 superscript 2 open parentheses x squared minus 5 x minus 6 close parentheses d x end cell row blank equals cell 3 open square brackets fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 5 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 6 x close square brackets subscript 0 superscript 2 end cell row blank equals cell 3 open square brackets 1 third x cubed minus 5 over 2 x squared minus 6 x close square brackets subscript 0 superscript 2 end cell row blank equals cell 3 open curly brackets open parentheses open parentheses 1 third cross times 2 cubed close parentheses minus open parentheses 5 over 2 cross times 2 squared close parentheses minus open parentheses 6 cross times 2 close parentheses close parentheses minus open parentheses open parentheses 1 third cross times 0 cubed close parentheses minus open parentheses 5 over 2 cross times 0 squared close parentheses minus open parentheses 6 cross times 0 close parentheses close parentheses close curly brackets end cell row blank equals cell 3 open curly brackets open parentheses 8 over 3 minus 10 minus 12 close parentheses minus open parentheses 0 minus 0 minus 0 close parentheses close curly brackets end cell row blank equals cell 3 open parentheses 8 over 3 minus 22 close parentheses end cell row blank equals cell 3 open parentheses 8 over 3 minus 66 over 3 close parentheses end cell row blank equals cell 3 open parentheses negative 58 over 3 close parentheses end cell row blank equals cell negative 58 end cell end table end style   

Jadi, jawaban yang tepat adalah D.space  

23

5.0 (1 rating)

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