CVXI5

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

We have dz=(1+2ti)dt, x=t, y=t^2\,.

=\int_0^1 (t^3+it^2)(1+2ti)dt\,

=\int_0^1 t^3 + 2it^4 + it^2 - 2t^3 \,dt = \frac{-1}{4}+i\frac{11}{15}\,


Main Page : Complex Variables : Complex Integrals

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