VC2.1

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\int f(t)\,dt=\int {(t-t^{2})i+2t^{3}j-3k}\,dt\,

=i\int (t-t^{2})\,dt+2j\int t^{3}\,dt-3k\int \,dt\,

=i[{\frac  {t^{2}}{2}}-{\frac  {t^{3}}{3}}]+{\frac  {t^{4}}{2}}j-3tk+c\, where c is an arbitrary constant vector.

ii).\int _{1}^{2}f(t)\,dt=\int _{1}^{2}{(t-t^{2})i+2t^{3}j-3k}\,dt\,

=i\int _{1}^{2}(t-t^{2})\,dt+2j\int _{1}^{2}t^{3}\,dt-3k\int _{1}^{2}\,dt\,

=i[{\frac  {t^{2}}{2}}-{\frac  {t^{3}}{3}}]+2j[{\frac  {t^{4}}{4}}]-3k[t]\, at [1,2]

=-{\frac  {5}{6}}i+{\frac  {15}{2}}j-3k\, (After Substituting the lower and upper values)

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