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Author: Tinku Tara

let-I-0-pi-4-e-2t-cos-4-t-dt-and-J-0-pi-4-e-2t-sin-4-tdt-1-calculate-I-J-and-I-J-2-find-the-value-of-I-and-J-

Question Number 66334 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{e}^{−\mathrm{2}{t}} \:{cos}^{\mathrm{4}} {t}\:{dt}\:{and}\:{J}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{e}^{−\mathrm{2}{t}} \:{sin}^{\mathrm{4}} {tdt} \\ $$$$\left.\mathrm{1}\right){calculate}\:\:{I}+{J}\:{and}\:{I}−{J} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{I}\:{and}\:{J}. \\…

1-2-1-3-1-4-1-

Question Number 798 by 123456 last updated on 15/Mar/15 $$\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\centerdot\centerdot\centerdot}}}} \\ $$ Answered by prakash jain last updated on 15/Mar/15 $$\mathrm{Ramanujan}'{s}\:\mathrm{Formula} \\ $$$${x}+\mathrm{1}=\sqrt{\mathrm{1}+{x}\sqrt{\mathrm{1}+\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}+\left({x}+\mathrm{2}\right)\sqrt{\mathrm{1}+…}}}} \\ $$$$\mathrm{For}\:{x}=\mathrm{2}…