Roboguru

Luas space daerah space yang space dibatasi space oleh space kurva space straight y equals straight x minus straight x squared comma space sumbu space straight x comma space garis space straight x equals 1 comma space dan space garis space straight x equals 2 space adalah space....

  1. 5 over 6 s a t u a n space l u a s

  2. 4 over 3 s a t u a n space l u a s

  3. 8 over 3 s a t u a n space l u a s

  4. 16 over 3 s a t u a n space l u a s

  5. 20 over 3 s a t u a n space l u a s

Jawaban:

Gambarkan space kurva space dengan space mencari space titik space potong space dengan space sumbu space straight X  straight y equals straight x minus straight x squared    Titik space potong space dengan space sumbu space straight X space yaitu space saat space straight y equals 0  straight x minus straight x squared equals 0  straight x left parenthesis 1 minus straight x right parenthesis equals 0  straight x equals 0 space atau space straight x equals 1    Ingat space bahwa space persamaan space kuadrat space ax squared plus bx plus straight c space dengan space straight a less than 0 space akan space berbentuk space  lengkungan space yang space menghadap space kebawah space left parenthesis memiliki space titik space maksimum right parenthesis

M e n g h i t u n g space l u a s space d a e r a h space d e n g a n space i n t e g r a l comma space  integral subscript b a t a s space k i r i end subscript superscript b a t a s space k a n a n end superscript k u r v a space a t a s minus k u r v a space b a w a h    M a k a  L equals integral subscript 1 superscript 2 0 minus left parenthesis x minus x squared right parenthesis d x space  L equals integral subscript 1 superscript 2 minus x plus x squared d x space  L equals right enclose negative 1 half x squared plus 1 third x cubed space end enclose subscript 1 superscript 2  L equals open parentheses negative 1 half left parenthesis 2 right parenthesis squared plus 1 third left parenthesis 2 right parenthesis cubed close parentheses minus open parentheses negative 1 half left parenthesis 1 right parenthesis squared plus 1 third left parenthesis 1 right parenthesis cubed close parentheses  L equals open parentheses negative 2 plus 8 over 3 close parentheses minus open parentheses negative 1 half plus 1 third close parentheses  L equals open parentheses 2 over 3 close parentheses minus open parentheses negative 1 over 6 close parentheses  L equals 5 over 6

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