si f, g y h son integrables, entonces las integrales indefinida y definida de una función vectorial r(t) = f(t)i + g(t)j + h(t)k se definen respectivamente por:
“ r(t) dt = [ “f(t) dt] i +[ “g(t) dt] + [ “h(t) dt]k
Ejemplo:
Si
R(t) = 6t2 i + 4e-2tj +8 cos 4tk
Entonces
“ r(t) dt = [6t2 dt]i + [ “ 4e-2t dt]j + [ “8 cos 4t dt]k
=[2t3 + c1]i + [−2e-2t +c2]j + [ “2 sen 4t + c3]k
=2t3i-2e-2tj + 2sen 4tk +C
Ejercicios:
3.-r(t)=ti+ 2tj + cos tk, t “0
z
y
x
15.- r(t) = < t cos t - sen t, t + cos t
=e2t (2t + 1)i + ˝ e-2tj + 1/2et2k +C