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k-1-1-k-1-sin-k-k-

Question Number 116965 by Dwaipayan Shikari last updated on 08/Oct/20 $$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} \:\frac{{sin}\left({k}\theta\right)}{{k}\theta} \\ $$ Answered by Bird last updated on 08/Oct/20 $${let}\:{g}\left({u}\right)\:=\sum_{{k}=\mathrm{1}} ^{\infty}…

e-3x-1-e-x-dx-

Question Number 51420 by Tawa1 last updated on 26/Dec/18 $$\int\:\:\frac{\mathrm{e}^{\mathrm{3x}} }{\mathrm{1}\:+\:\mathrm{e}^{\mathrm{x}} }\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 26/Dec/18 $${let}\:\:\mathrm{1}+{e}^{{x}} \:=\:{t}\:\:\:,\:\Rightarrow\:\:{e}^{{x}} {dx}\:=\:{dt} \\…

A-B-C-D-is-a-parallelogram-on-the-Argand-plane-The-affixes-of-A-B-C-are-8-5i-7-5i-5-5i-respectively-Find-the-affix-of-D-

Question Number 51321 by Tawa1 last updated on 25/Dec/18 $$\mathrm{A}\:\mathrm{B}\:\mathrm{C}\:\mathrm{D}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{parallelogram}\:\mathrm{on}\:\mathrm{the}\:\mathrm{Argand}\:\mathrm{plane}.\:\mathrm{The}\: \\ $$$$\mathrm{affixes}\:\mathrm{of}\:\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\:\mathrm{are}\:\:\:\mathrm{8}\:+\:\mathrm{5i},\:\:−\:\mathrm{7}\:−\:\mathrm{5i},\:\:−\:\mathrm{5}\:+\:\mathrm{5i}\:\:\mathrm{respectively} \\ $$$$.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{affix}\:\mathrm{of}\:\:\mathrm{D} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 26/Dec/18 $${A}\left(\mathrm{8},\mathrm{5}\right)\:\:{B}\left(−\mathrm{7},−\mathrm{5}\right)\:{C}\left(−\mathrm{5},\mathrm{5}\right)\:{D}\left({x},{y}\right) \\…