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Tentukanlah nilai integral di bawah ini: d. ∫−11​(5−2x−6x2) dx

Pertanyaan

Tentukanlah nilai integral di bawah ini:

d. integral subscript negative 1 end subscript superscript 1 open parentheses 5 minus 2 x minus 6 x squared close parentheses space d x space 

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

 integral subscript negative 1 end subscript superscript 1 open parentheses 5 minus 2 x minus 6 x squared close parentheses space d x equals 6.

Pembahasan

Ingat!

  table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses space d x end cell equals cell integral subscript a superscript b f open parentheses x close parentheses space d x plus-or-minus integral subscript a superscript b g open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b k f left parenthesis x right parenthesis space d x end cell equals cell k integral subscript a superscript b f left parenthesis x right parenthesis space d x end cell row cell integral subscript a superscript b a x to the power of n space d x end cell equals cell open parentheses fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent close parentheses subscript a superscript b space end cell end table 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript negative 1 end subscript superscript 1 open parentheses 5 minus 2 x minus 6 x squared close parentheses space d x end cell row blank equals cell integral subscript negative 1 end subscript superscript 1 5 space d x minus 2 integral subscript negative 1 end subscript superscript 1 x space d x minus 6 integral subscript negative 1 end subscript superscript 1 x squared space d x end cell row blank equals cell open parentheses fraction numerator 5 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent close parentheses subscript negative 1 end subscript superscript 1 minus 2 open parentheses fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent close parentheses subscript negative 1 end subscript superscript 1 minus 6 open parentheses fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent close parentheses subscript negative 1 end subscript superscript 1 end cell row blank equals cell 5 open parentheses x close parentheses subscript negative 1 end subscript superscript 1 minus 2 times 1 half open parentheses x squared close parentheses subscript negative 1 end subscript superscript 1 minus 6 times 1 third open parentheses x cubed close parentheses subscript negative 1 end subscript superscript 1 end cell row blank equals cell 5 open parentheses x close parentheses subscript negative 1 end subscript superscript 1 minus open parentheses x squared close parentheses subscript negative 1 end subscript superscript 1 minus 2 open parentheses x cubed close parentheses subscript negative 1 end subscript superscript 1 end cell row blank equals cell 5 open parentheses 1 minus open parentheses negative 1 close parentheses close parentheses minus open parentheses 1 squared minus open parentheses negative 1 close parentheses squared close parentheses minus 2 open parentheses 1 cubed minus open parentheses negative 1 close parentheses cubed close parentheses end cell row blank equals cell 5 times 2 minus 0 minus 2 times 2 end cell row blank equals cell 10 minus 4 end cell row blank equals 6 end table   

Jadi, integral subscript negative 1 end subscript superscript 1 open parentheses 5 minus 2 x minus 6 x squared close parentheses space d x equals 6.

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