Matematika

Pertanyaan

tolong bantu jawab soal no 1 ttg volume benda putar dengan cara penyelesaiannya
tolong bantu jawab soal no 1 ttg volume benda putar dengan cara penyelesaiannya

1 Jawaban

  • cari batas integral
    x² - 2x = 0
    x(x - 2) = 0
    x = 0   dan   x = 2
    ===========================
    L = π ∫ y² dx {0...2}

    = π ∫ (x² - 2x)² dx {0...2}
    = π ∫ x⁴ - 4x³ + 4x²  dx {0...2}
    = π [ x⁵/5 - x⁴ + 4x³/3 ] {2...0}
    = π [2⁵/5 - 2⁴ + 4(2³)/3 - 0]
    = π [6(2⁴)/15 + 10(2⁴)/15 - 15(2⁴)/15]
    = π [2⁴/15]
    = (16/15) π satuan volume