Timeline for How to calculate an integral by deforming the path
Current License: CC BY-SA 3.0
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| Dec 18, 2016 at 5:44 | comment | added | J. M.'s missing motivation♦ |
Note that Integrate[] and NIntegrate[] are both perfectly capable of traversing piecewise-linear contours on their own: NIntegrate[Cos[z]/((z + 2)*(z + I) (z - 2 I)), {z, -3/2 - 2 I, 3/2 - 2 I, 3/2 + 3 I, -3/2 + 3 I, -3/2 - 2 I}]. Just be sure to close the loop. For reference, here's the symbolic result from that approach after simplifying: $$-\frac{\pi}{60e^2}(1+3i)\left((2-2i)e\left(1+e^2\right)+(1+2i)\left(1+e^4\right)\right)$$
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| Dec 18, 2016 at 5:27 | history | answered | LouisB | CC BY-SA 3.0 |