CVXI4

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Evaluate \int_C (xy+ix^2)dz, C=z(t)=t+it, 0\le t\le 1\,.

We have dz = (1+i)dt\, and x=t, y=t\,.

The integral is

\int_0^1(t^2+it^2)(1+i)dt\,

=\int_0^1 t^2 (1+i)^2 \,dt = 2i \int_0^1 t^2 dt = \frac{2i}{3}\,


Main Page : Complex Variables : Complex Integrals

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