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Category: Integration

Question-26125

Question Number 26125 by offrinshingal last updated on 20/Dec/17 Commented by abdo imad last updated on 21/Dec/17 $$\int_{{R}} \frac{{x}\:{e}^{{irx}} }{\left({x}^{\mathrm{2}} −{k}^{\mathrm{2}} \right)}{dx}\:−\:\int_{{R}} \:\frac{{x}\:{e}^{−{irx}} }{\left({x}^{\mathrm{2}} −\:{k}^{\mathrm{2}}…

answer-to-26024-let-put-c-0-cos-ax-2-dx-and-c-0-sin-ax-2-dx-ew-have-c-is-0-e-iax-2-dx-2-1-R-e-iax-2-dx-and-i-put-x-1-2-r-x-notation-

Question Number 26107 by abdo imad last updated on 19/Dec/17 answerto26024letputc=0cos(ax2)dxandc=0sin(ax2)dx$${ew}\:{have}\:\:{c}−{is}\:\:=\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{iax}^{\mathrm{2}} } {dx}\:\:\:=\mathrm{2}^{−\mathrm{1}} \:\:\int_{{R}} \:{e}^{−{iax}^{\mathrm{2}}…