Question Number 220673 by SdC355 last updated on 17/May/25
$$\mathrm{evaluate} \\ $$$$\mathrm{1}.\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{cos}\left({mt}\right)}{{t}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{t} \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}\left({z}^{\mathrm{2}} \right)\:\mathrm{d}{z}\:\mathrm{and}\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{cos}\left({z}^{\mathrm{2}} \right)\:\mathrm{d}{z} \\ $$$${by}\:{using}\:{complex}\:{integral}.. \\ $$