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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