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0-2pi-z-sin-z-1-cos-2-z-dz-Contour-integral-z-2-1-z-2-1-dz-z-2-sin-z-z-2-1-dz-




Question Number 213484 by issac last updated on 06/Nov/24
∫_0 ^( 2π)  ((z∙sin(z))/(1+cos^2 (z)))dz  (Contour integral)   ∮_( ∣z∣=2)  (1/(z^2 +1)) dz  ∮_( ∣z∣=2)   ((sin(z))/(z^2 +1)) dz
$$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \:\frac{{z}\centerdot\mathrm{sin}\left({z}\right)}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left({z}\right)}\mathrm{d}{z}\:\:\left(\mathrm{Contour}\:\mathrm{integral}\right)\: \\ $$$$\oint_{\:\mid{z}\mid=\mathrm{2}} \:\frac{\mathrm{1}}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$$$\oint_{\:\mid{z}\mid=\mathrm{2}} \:\:\frac{\mathrm{sin}\left({z}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$

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