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Pertanyaan

Volume benda putar yang terjadi bila daerah yang dibatasi oleh kurva y equals 4 minus x squared dan garis y = x + 2 diputar mengelilingi sumbu X sejauh 360 degree adalah....

  1. 12 straight pi satuan volume

  2. 72 over 5 straight pi satuan volume

  3. 18 straight pi satuan volume

  4. 92 over 5 straight pi satuan volume

  5. 108 over 5 straight pi satuan volume

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

Pertama – tama space cari space titik space potong space garis space dan space kurva  straight y equals straight y  straight x plus 2 equals 4 minus straight x squared  straight x squared plus straight x minus 2 equals 0  open parentheses straight x plus 2 close parentheses open parentheses straight x minus 1 close parentheses equals 0  straight x equals negative 2 logical or straight x equals 1  Perhatikan space gambar space berikut

Maka space bentuk space integral space yang space sesuai space adalah  straight pi integral subscript negative 2 end subscript superscript 1 open parentheses 4 minus straight x squared close parentheses squared minus open parentheses straight x plus 2 close parentheses squared straight space dx  equals straight pi integral subscript negative 2 end subscript superscript 1 open parentheses 16 minus 8 straight x squared plus straight x to the power of 4 close parentheses minus open parentheses straight x squared plus 4 straight x plus 4 close parentheses straight space dx  equals straight pi integral subscript negative 2 end subscript superscript 1 open parentheses straight x to the power of 4 minus 9 straight x squared minus 4 straight x plus 12 close parentheses dx  equals straight pi open square brackets 1 fifth straight x to the power of 5 minus 3 straight x cubed minus 2 straight x squared plus 12 straight x close square brackets subscript negative 2 end subscript superscript 1  equals straight pi open curly brackets open parentheses 1 fifth left parenthesis 1 right parenthesis to the power of 5 minus 3 left parenthesis 1 right parenthesis cubed minus 2 left parenthesis 1 right parenthesis squared plus 12 left parenthesis 1 right parenthesis close parentheses minus open parentheses 1 fifth left parenthesis negative 2 right parenthesis to the power of 5 minus 3 left parenthesis negative 2 right parenthesis cubed minus 2 left parenthesis negative 2 right parenthesis squared plus 12 left parenthesis negative 2 right parenthesis close parentheses close curly brackets  equals straight pi open curly brackets open parentheses 1 fifth minus 3 minus 2 plus 12 close parentheses minus open parentheses fraction numerator negative 32 over denominator 5 end fraction plus 24 minus 8 minus 24 close parentheses close curly brackets  equals straight pi open curly brackets open parentheses 36 over 5 close parentheses minus open parentheses fraction numerator negative 72 over denominator 5 end fraction close parentheses close curly brackets  equals 108 over 5 straight pi

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Volume daerah yang dibatasi kurva y=2x2 dan y = 4x bila diputar mengelilingi sumbu X sejauh 360∘ adalah.....

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