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Luas daerah antara kurva y = x 3 − x 2 − 6 x dan sumbu X adalah ....

Luas daerah antara kurva dan sumbu X adalah ....

  1. begin mathsize 14px style 23 5 over 12 end style satuan luas

  2. begin mathsize 14px style 23 1 over 12 end style satuan luas

  3. begin mathsize 14px style 22 3 over 12 end style satuan luas

  4. begin mathsize 14px style 21 5 over 12 end style satuan luas

  5. begin mathsize 14px style 21 1 over 12 end style satuan luas

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S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

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begin mathsize 14px style straight y equals straight x cubed minus straight x squared minus 6 straight x  straight y equals straight x open parentheses straight x squared minus straight x minus 6 close parentheses  straight y equals straight x open parentheses straight x minus 3 close parentheses left parenthesis straight x plus 2 right parenthesis    Titik space potong space sumbu space straight x space didapat space ketika space straight y space equals space 0  straight x open parentheses straight x minus 3 close parentheses open parentheses straight x plus 2 close parentheses equals 0  straight x subscript 1 equals 0 comma space straight x subscript 2 equals 3 space dan space straight x subscript 3 equals negative 2    Perhatikan space gambar space factorial end style

begin mathsize 14px style Luas space daerah space dapat space dicari space dengan space menghitung space colon  straight L subscript straight I plus straight L subscript II  equals integral subscript negative 2 end subscript superscript 0 open parentheses straight x cubed minus straight x squared minus 6 straight x close parentheses dx plus integral subscript 0 superscript 3 minus open parentheses straight x cubed minus straight x squared minus 6 straight x close parentheses dx  equals open square brackets 1 fourth x to the power of 4 minus 1 third x cubed minus 3 x squared close square brackets subscript negative 2 end subscript superscript 0 plus open square brackets negative 1 fourth x to the power of 4 plus 1 third x cubed plus 3 x squared close square brackets subscript 0 superscript 3  equals open curly brackets open parentheses 1 fourth left parenthesis 0 right parenthesis to the power of 4 minus 1 third left parenthesis 0 right parenthesis cubed minus 3 left parenthesis 0 right parenthesis squared close parentheses minus open parentheses 1 fourth left parenthesis negative 2 right parenthesis to the power of 4 minus 1 third left parenthesis negative 2 right parenthesis cubed minus 3 left parenthesis negative 2 right parenthesis squared close parentheses close curly brackets  space space space space plus open curly brackets open parentheses negative 1 fourth left parenthesis 3 right parenthesis to the power of 4 plus 1 third left parenthesis 3 right parenthesis cubed plus 3 left parenthesis 3 right parenthesis squared close parentheses minus open parentheses negative 1 fourth left parenthesis 0 right parenthesis to the power of 4 plus 1 third left parenthesis 0 right parenthesis cubed plus 3 left parenthesis 0 right parenthesis squared close parentheses close curly brackets  equals open curly brackets 0 minus open parentheses 4 plus 8 over 3 minus 12 close parentheses close curly brackets plus open curly brackets open parentheses negative 81 over 4 plus 9 plus 27 close parentheses close curly brackets  equals 16 over 3 plus 63 over 4  equals fraction numerator 64 plus 189 over denominator 12 end fraction  equals 253 over 12  equals 21 1 over 12 space satuan space luas end style

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Luas daerah yang dibatasi oleh kurva y = x 2 − x − 2 dengan garis y = − 4 x + 2 adalah ... satuan luas.

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