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Category: Integration

calculate-e-z-z-1-z-3-2-dz-with-id-the-positif-circle-z-C-z-3-2-

Question Number 28990 by abdo imad last updated on 02/Feb/18 $${calculate}\:\int_{\gamma} \:\:\:\frac{{e}^{{z}} }{\left({z}−\mathrm{1}\right)\left({z}+\mathrm{3}\right)^{\mathrm{2}} }{dz}\:{with}\:\gamma\:{id}\:{the}\:{positif} \\ $$$${circle}\:\gamma=\left\{{z}\in{C}/\:\mid{z}\mid=\frac{\mathrm{3}}{\mathrm{2}}\right\}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

let-give-I-m-a-0-cos-mx-1-x-2-x-2-a-2-dx-1-verify-that-I-m-1-lim-a-1-I-m-a-2-find-the-value-of-0-x-sin-mx-1-x-2-2-dx-

Question Number 28985 by abdo imad last updated on 02/Feb/18 $${let}\:{give}\:{I}_{{m},{a}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({mx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{dx} \\ $$$$\left.\mathrm{1}\right){verify}\:{that}\:{I}_{{m},\mathrm{1}} ={lim}_{{a}\rightarrow\mathrm{1}} \:{I}_{{m},{a}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{sin}\left({mx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}}…