A integral definida da função vetorial r(t) = (t² - 1)i + (2t +1)j + (t³)k para t pertencente ao intervalo [0,2] é:

\(\Longrightarrow \,\, \Big < \, \int \limits_0^2 (t^2-1)dt\, , \, \int \limits_0^2 (2t+1)dt \, , \, \int \limits_0^2t^3 \,dt \, \Big >\)

\(\Longrightarrow \,\, \Big < \, ({1 \over 3}t^3-t) \bigg | _0^2\, , \, (t^2+t)\bigg | _0^2 \, , \, {1 \over 4}(t^4) \bigg | _0^2 \, \Big >\)

\(\Longrightarrow \,\, \Big < \, ({1 \over 3}(2)^3-2) - ({1 \over 3}(0)^3-0)\, , \, (2^2+2)-(0^2+0) \, , \, {1 \over 4}(2)^4-{1 \over 4}(0)^4\, \Big >\)

\(\Longrightarrow \,\, \Big < \, ({8 \over 3}-2) - 0\, , \, (4+2)-0 \, , \, {16 \over 4}-0\, \Big >\)

\(\Longrightarrow \fbox {$ \,\, \Big < \, {2 \over 3}\, , \, 6 \, , \, 4\, \Big > $}\)