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Nilai dari ∫ 3 7 ​ 2 ∣ x − 6 ∣ d x adalah....

Nilai dari  adalah....

  1. 14

  2. 18

  3. 25

  4. 32

  5. 35

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M. Robo

Master Teacher

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Pembahasan

Ingat definisi nilai mutlak sebagai berikut Maka Atau Sehingga Pada interval didapat , sehingga Maka

Ingat definisi nilai mutlak sebagai berikut

vertical line x vertical line equals open curly brackets table attributes columnalign left end attributes row cell x comma space j i k a space x greater or equal than 0 end cell row cell negative x comma space j i k a space x less than 0 end cell end table close

Maka

2 open vertical bar x minus 6 close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell 2 left parenthesis x minus 6 right parenthesis comma space j i k a space 2 left parenthesis x minus 6 right parenthesis greater or equal than 0 end cell row cell negative 2 left parenthesis x minus 6 right parenthesis. space j i k a space 2 left parenthesis x minus 6 right parenthesis less than 0 end cell end table close

Atau

2 vertical line x minus 6 vertical line equals open curly brackets table attributes columnalign left end attributes row cell 2 left parenthesis x minus 6 right parenthesis comma space j i k a space x greater or equal than 6 end cell row cell negative 2 left parenthesis x minus 6 right parenthesis comma space j i k a space x less than 6 end cell end table close

Sehingga

integral subscript 3 superscript 7 2 vertical line x minus 6 vertical line d x equals integral subscript 3 superscript 6 2 vertical line x minus 6 vertical line d x plus integral subscript 6 superscript 7 2 vertical line x minus 6 vertical line d x

Pada interval 3 less or equal than x less than 6 spacedidapat 2 vertical line x minus 6 vertical line equals negative 2 left parenthesis x minus 6 right parenthesis, sehingga

integral subscript 6 superscript 7 2 vertical line x minus 6 vertical line d x equals 2 integral subscript 6 superscript 7 left parenthesis x minus 6 right parenthesis d x equals 2 left parenthesis ├ x squared minus 6 x right square bracket subscript 6 superscript 7 right parenthesis equals 2 left parenthesis 7 plus 0 right parenthesis equals 14

Maka

integral from 3 to 7 of 2 open vertical bar x minus 6 close vertical bar d x equals integral from 3 to 6 of 2 open vertical bar x minus 6 close vertical bar d x plus integral from 6 to 7 of 2 open vertical bar x minus 6 close vertical bar d x equals 18 plus 14 equals 32  

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