volume benda yg terjadi jika daerah yang dibatasi kurva y = 3x + 2, garis x = 1 dan x = 4 diputar mengelilingi sumbu x sejauh 360°
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ngopi banh
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aplikasi integral
volume
cara 1
volume
= π ∫y² dx [4 1]
= π ∫(3x + 2)² dx
= π ∫(9x² + 12x + 4) dx
= π (3x³ + 6x² + 4x)
= π (3(4³ – 1³) + 6(4² – 1²) + 4(4 – 1))
= π (189 + 90 + 12)
= 291 satuan volume
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cara 2
a = ∆x = 4 – 1 = 3
x = 4 → y = R = 3.4 + 2 = 14
x = 1 → y = r = 3.1 + 2 = 5
volume kerucut terpancung
= 1/3 πa (rR + r² + R²)
= 1/3 π . 3(5.14 + 5² + 14²)
= π (70 + 25 + 196)
= 291π satuan volume