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Pertanyaan

Daerah R dibatasi oleh y equals a square root of x comma y equals a x squared, untuk x element of open square brackets 0 comma 2 close square brackets. Jika volume benda padat yang didapat dengan memutar R terhadap sumbu x adalah 5 straight pi, maka a=...

  1. -5

  2. -4

  3. -3

  4. -2

  5. -1

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Ilustrasi gambar :

     

     M a k a space d a e r a h space p a d a space s o a l space a d a l a h  V subscript t o t a l end subscript equals V subscript 1 plus V subscript I I end subscript  5 pi equals pi integral subscript 0 superscript 1 open parentheses open parentheses a square root of x close parentheses squared minus open parentheses a x squared close parentheses squared close parentheses d x plus pi integral subscript 1 superscript 2 open parentheses open parentheses a x squared close parentheses squared minus open parentheses a square root of x close parentheses squared close parentheses d x  5 equals integral subscript 0 superscript 1 open parentheses a squared x minus a squared x to the power of 4 close parentheses d x integral subscript 1 superscript 2 open parentheses a squared x to the power of 4 minus a squared x close parentheses d x  5 equals a squared over 2 x squared minus a squared over 5 x to the power of 5 open table row 1 row 0 end table close square brackets plus a squared over 5 x to the power of 5 minus a squared over 2 x squared open table row 2 row 1 end table close square brackets  5 equals a squared over 2 open parentheses 1 close parentheses squared minus a squared over 5 open parentheses 1 close parentheses to the power of 5 plus open parentheses open parentheses a squared over 5 open parentheses 2 close parentheses to the power of 5 minus a squared over 2 open parentheses 2 close parentheses squared close parentheses minus open parentheses a squared over 5 open parentheses 1 close parentheses to the power of 5 minus a squared over 2 open parentheses 1 close parentheses squared close parentheses close parentheses  5 equals a squared over 2 minus a squared over 5 plus fraction numerator 32 a squared over denominator 5 end fraction minus 2 a squared minus a squared over 5 plus a squared over 2  5 a squared equals 5  a squared equals 1  a equals plus-or-minus 1

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Daerah R dibatasi oleh y=bx​, y = bx, untuk x ∈ [0,2]. Jika volume benda padat yang didapat dengan memutar R terhadap sumbu x adalah π, maka b = ....

9

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