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Pertanyaan

Hiutnglah nilai integral berikut:

b. integral subscript 1 superscript 3 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x minus integral subscript 4 superscript 3 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x space 

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Mahasiswa/Alumni Universitas Indraprasta PGRI

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Jawaban

 integral subscript 1 superscript 3 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x minus integral subscript 4 superscript 3 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x equals 49 1 half.

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 open parentheses x close parentheses space d x end cell equals cell k integral subscript a superscript b f open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b f open parentheses x close parentheses space d x end cell equals cell integral subscript a superscript k f open parentheses x close parentheses space d x plus integral subscript k superscript b f open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b f open parentheses x close parentheses space d x end cell equals cell integral subscript a superscript k f open parentheses x close parentheses space d x minus integral subscript b superscript k f open parentheses x close parentheses 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 end cell end table    

Sehingga,

    table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 1 superscript 3 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x minus integral subscript 4 superscript 3 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x end cell row blank equals cell integral subscript 1 superscript 4 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x end cell row blank equals cell integral subscript 1 superscript 4 open parentheses 3 x squared minus x minus 2 close parentheses space d x end cell row blank equals cell 3 integral subscript 1 superscript 4 x squared space d x minus integral subscript 1 superscript 4 x space d x minus integral subscript 1 superscript 4 2 space d x end cell row blank equals cell 3 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 1 superscript 4 minus 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 1 superscript 4 minus open parentheses fraction numerator 2 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent close parentheses subscript 1 superscript 4 end cell row blank equals cell open parentheses x cubed close parentheses subscript 1 superscript 4 minus 1 half open parentheses x squared close parentheses subscript 1 superscript 4 minus 2 open parentheses x close parentheses subscript 1 superscript 4 end cell row blank equals cell open parentheses 4 cubed minus 1 cubed close parentheses minus 1 half open parentheses 4 squared minus 1 squared close parentheses minus 2 open parentheses 4 minus 1 close parentheses end cell row blank equals cell 63 minus 15 over 2 minus 6 end cell row blank equals cell 57 minus 15 over 2 end cell row blank equals cell fraction numerator 114 minus 15 over denominator 2 end fraction end cell row blank equals cell 99 over 2 end cell row blank equals cell 49 1 half end cell end table 

Jadi, integral subscript 1 superscript 3 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x minus integral subscript 4 superscript 3 open parentheses 3 x plus 2 close parentheses open parentheses x minus 1 close parentheses space d x equals 49 1 half.

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