Question

Volume benda putar yang dibatasi kurva y = x² dan y = x³

Answer 1

Verified answer

RALAT!!
V = π ₀∫¹ (x²)²- (x³)² dx
V = π ₀∫¹ x⁴ - x⁶ dx
V=π [ |x⁵/5 - x⁷/7|₀¹ ]
V=π [ (1/5 - 1/7) - 0]
V=π [2/35]
V=2π/35 satuan luas

Answer 2

Verified answer

Volume Benda Putar mengeliling sumbu x
V = π ∫ y² dx

y1 = x²
y2 = x³
batas integral untuk x ,
y1 - y2 = 0
x² - x³  = 0 -> x²(1 - x) = 0
x = 0 atau x = 1

V = π ₀¹∫ (y1)² - (y2)² dx
V = π ₀¹∫ (x²)²-(x³)² dx
V = π ₀¹∫ x⁴ - x⁶ dx = [1/5 x⁵ - 1/7 x⁷]¹₀
V = π [1/5 - 1/7]
V = (2/35)π  satuan volume