This applet is a variant of Applet 6, Complex Integration. The function is now specified by locating its poles and residues. Also, the integral has been divided by 2 pi in order to make the residue theorem clearer.
Note that every time a contour goes anti-clockwise around a pole, the integral increases by 2 pi i times the residue at that pole. Similarly if a contour winds once clockwise around a pole, the integral decreases by 2 pi i times the residue at that pole. Try making a function with several poles at different places, and testing contours that go around several poles, or go around different poles a different number of times.
NB: There will be an inaccuracy of about +- 5% in the final integral,
basically because all integrals are being computed numerically (in fact,
I'm using the so-called Midpoint Rule). The inaccuracy gets especially
bad if the contour gets too close to a pole.