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Hasil dari ∫ − 2 1 ​ ( x 3 − 6 x 2 + 8 + 2 ) d x = …

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H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

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hasil dari .

hasil dari integral subscript negative 2 end subscript superscript 1 open parentheses x cubed minus 6 x squared plus 8 plus 2 close parentheses d x equals negative 111 over 4

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Pembahasan

Rumus integral tentu adalah sebagai berikut: Sehingga, hasil dari didapatkan: Jadi, hasil dari .

Rumus integral tentu adalah sebagai berikut:

integral subscript a superscript b f open parentheses x close parentheses d x equals open square brackets F open parentheses x close parentheses close square brackets subscript a superscript b equals F open parentheses b close parentheses minus F open parentheses a close parentheses 

Sehingga, hasil dari integral subscript negative 2 end subscript superscript 1 open parentheses x cubed minus 6 x squared plus 8 plus 2 close parentheses d x didapatkan:

  begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript negative 2 end subscript superscript 1 open parentheses x cubed minus 6 x squared plus 8 x plus 2 close parentheses d x end cell row blank equals cell open square brackets fraction numerator 1 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent minus fraction numerator 6 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus fraction numerator 8 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus 2 x close square brackets subscript negative 2 end subscript superscript 1 end cell row blank equals cell open square brackets 1 fourth x to the power of 4 minus 6 over 3 x cubed plus 8 over 2 x squared plus 2 x close square brackets subscript negative 2 end subscript superscript 1 end cell row blank equals cell open square brackets 1 fourth x to the power of 4 minus 2 x cubed plus 4 x squared plus 2 x close square brackets subscript negative 2 end subscript superscript 1 end cell row blank equals cell open square brackets 1 fourth open parentheses 1 close parentheses to the power of 4 minus 2 open parentheses 1 close parentheses cubed plus 4 open parentheses 1 close parentheses squared plus 2 open parentheses 1 close parentheses close square brackets minus open square brackets 1 fourth open parentheses negative 2 close parentheses to the power of 4 minus 2 open parentheses negative 2 close parentheses cubed plus 4 open parentheses negative 2 close parentheses squared plus 2 open parentheses negative 2 close parentheses close square brackets end cell row blank equals cell open square brackets 1 fourth open parentheses 1 close parentheses minus 2 open parentheses 1 close parentheses plus 4 open parentheses 1 close parentheses plus 2 open parentheses 1 close parentheses close square brackets minus open square brackets 1 fourth open parentheses 16 close parentheses minus 2 open parentheses negative 8 close parentheses plus 4 open parentheses 4 close parentheses plus 2 open parentheses negative 2 close parentheses close square brackets end cell row blank equals cell open square brackets 1 fourth minus 2 plus 4 plus 2 close square brackets minus open square brackets 4 plus 16 plus 16 minus 4 close square brackets end cell row blank equals cell open square brackets 17 over 4 close square brackets minus open square brackets 32 close square brackets end cell row blank equals cell negative 111 over 4 end cell end table end style   

Jadi, hasil dari integral subscript negative 2 end subscript superscript 1 open parentheses x cubed minus 6 x squared plus 8 plus 2 close parentheses d x equals negative 111 over 4

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