Integrali curvilinei in R3
(x(t), y(t), z(t))
f(t) = (x(t), y(t), z(t))
A
x(t) = (1 - t) xA + t xB
y(t) = (1 - t) yA + t yB
z(t) = (1 - t) zA + t zB
L'elicoide
x = r cos t
y = r sin t
z = t
t ∈ [0, 2π]
∫AB ds = ∫ab √(x'2 + y'2 + z'2) dt = ∫02π √(r2 sin2t + r2 cos2t + 1) dt = ∫02π √(r2 + 1) dt = 2π √(r2 + 1)
Integrali curvilinei in R3
f(t) = (x(t), y(t), z(t))
A
x(t) = (1-t) xA + t xB
y(t) = (1-t) yA + t yB
z(t) = (1-t) zA + t zB
L'elicoide
x = r cos t
y = r sin t
z = t
t ∈ [0, 2π]
∫γ ds = ∫ab √(x'2 + y'2 + z'2) dt = ∫02π √(r2 sin2t + r2 cos2t + 1) dt = ∫02π √r2 + 1 dt = 2π √r2 + 1