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∫ − 3 3 ​ ( x − [ x ]) d x

 

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Jawaban terverifikasi

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 integral subscript negative 3 end subscript superscript 3 left parenthesis x minus left square bracket x right square bracket right parenthesis d x equals 3.

Pembahasan

Pembahasan
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menyatakan bilangan bulat terbesar yang kurang dari atau sama dengan . Jadi, .

left square bracket x right square bracket menyatakan bilangan bulat terbesar yang kurang dari atau sama dengan x.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript negative 3 end subscript superscript 3 left parenthesis x minus left square bracket x right square bracket right parenthesis d x end cell row blank equals cell integral subscript negative 3 end subscript superscript 3 x space straight d x minus integral subscript negative 3 end subscript superscript 3 open square brackets x close square brackets d x end cell row blank equals cell integral subscript negative 3 end subscript superscript 3 x space straight d x minus open parentheses integral subscript negative 3 end subscript superscript negative 2 end superscript open square brackets x close square brackets d x plus integral subscript negative 2 end subscript superscript negative 1 end superscript open square brackets x close square brackets d x plus integral subscript negative 1 end subscript superscript 0 open square brackets x close square brackets d x plus integral subscript 0 superscript 1 open square brackets x close square brackets d x plus integral subscript 1 superscript 2 open square brackets x close square brackets d x plus integral subscript 2 superscript 3 open square brackets x close square brackets d x close parentheses end cell row blank equals cell integral subscript negative 3 end subscript superscript 3 x space straight d x minus open parentheses integral subscript negative 3 end subscript superscript negative 2 end superscript open parentheses negative 3 close parentheses d x plus integral subscript negative 2 end subscript superscript negative 1 end superscript open parentheses negative 2 close parentheses d x plus integral subscript negative 1 end subscript superscript 0 open parentheses negative 1 close parentheses d x plus integral subscript 0 superscript 1 open parentheses 0 close parentheses d x plus integral subscript 1 superscript 2 open parentheses 1 close parentheses d x plus integral subscript 2 superscript 3 open parentheses 2 close parentheses d x close parentheses end cell row blank equals cell open parentheses 1 half x squared close parentheses subscript negative 3 end subscript superscript 3 minus open parentheses open parentheses negative 3 x close parentheses subscript negative 3 end subscript superscript negative 2 end superscript plus open parentheses negative 2 x close parentheses subscript negative 2 end subscript superscript negative 1 end superscript plus open parentheses negative x close parentheses subscript negative 1 end subscript superscript 0 plus 0 plus open parentheses x close parentheses subscript 1 superscript 2 plus open parentheses 2 x close parentheses subscript 2 superscript 3 close parentheses end cell row blank equals cell open parentheses 1 half left parenthesis 3 right parenthesis squared minus 1 half left parenthesis negative 3 right parenthesis squared close parentheses minus end cell row blank blank cell open parentheses negative 3 left parenthesis negative 2 minus left parenthesis negative 3 right parenthesis right parenthesis plus left parenthesis negative 2 right parenthesis left parenthesis negative 1 minus left parenthesis negative 2 right parenthesis right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 0 minus left parenthesis negative 1 right parenthesis right parenthesis plus 0 plus 1 left parenthesis 2 minus 1 right parenthesis plus 2 left parenthesis 3 minus 2 right parenthesis close parentheses end cell row blank equals cell open parentheses 9 over 2 minus 9 over 2 close parentheses minus left parenthesis negative 3 minus 2 minus 1 plus 1 plus 2 right parenthesis end cell row blank equals cell 0 plus 3 end cell row blank equals 3 end table end style 

Jadi, integral subscript negative 3 end subscript superscript 3 left parenthesis x minus left square bracket x right square bracket right parenthesis d x equals 3.

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