VC2.2

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\int _{0}^{1}f(t)\,dt=\int _{0}^{1}{ti+(t^{2}-2t)j+(3t^{2}+3t^{3})k}\,dt\,

=i\int _{0}^{1}t\,dt+j\int _{0}^{1}(t^{2}-2t)\,dt+k\int _{0}^{1}(3t^{2}+3t^{3})\,dt\,

=i[{\frac  {t^{2}}{2}}]+j[{\frac  {t^{3}}{3}}-t^{2}]+k[t^{3}+{\frac  {3t^{4}}{4}}]\, at (0,1)

=i[{\frac  {1}{2}}+j[{\frac  {1}{3}}-1]+k[1+{\frac  {3}{4}}]={\frac  {1}{2}}i-{\frac  {2}{3}}j+{\frac  {7}{4}}k\,

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