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Category: Integration

e-u-cos-u-sin-u-e-u-du-

Question Number 215498 by alephnull last updated on 08/Jan/25 $$\int\left({e}^{−\omega{u}} +\mathrm{cos}\left({u}\right)−\frac{\mathrm{sin}\left(\omega{u}\right)}{{e}^{{u}} }\right){du} \\ $$ Answered by MathematicalUser2357 last updated on 10/Jan/25 $$−\frac{{e}^{−{u}\omega} }{\omega}+\frac{{e}^{−{u}} \mathrm{sin}\:{u}\omega}{\left(\omega−{i}\right)\left(\omega+{i}\right)}+\frac{{e}^{−{u}} \omega\mathrm{cos}\:{u}\omega}{\left(\omega−{i}\right)\left(\omega+{i}\right)}+\mathrm{sin}\:{u}+{C}…

sin-3-x-2-sec-x-2-cos-3-x-cos-2-x-cosx-dx-Solve-this-integral-

Question Number 215414 by MATHEMATICSAM last updated on 06/Jan/25 $$\int\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sec}\left(\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}{x}}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{this}\:\mathrm{integral}. \\ $$ Commented by JamesZhou last updated on 06/Jan/25 $${maybe}\:{numerator}\:{issi}\hat…

The-following-diagram-shows-the-relationship-between-electromotive-force-e-m-f-and-the-time-t-in-a-dynamo-coil-During-the-time-interval-from-t-0-to-t-1-30-seconds-the-average-electromotive-f

Question Number 215410 by York12 last updated on 05/Jan/25 $$\mathrm{The}\:\mathrm{following}\:\mathrm{diagram}\:\mathrm{shows}\:\mathrm{the}\:\mathrm{relationship} \\ $$$$\mathrm{between}\:\mathrm{electromotive}\:\mathrm{force}\:\left(\mathrm{e}.\mathrm{m}.\mathrm{f}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{time}\:\left(\mathrm{t}\right)\:\mathrm{in}\:\mathrm{a}\:\mathrm{dynamo} \\ $$$$\mathrm{coil}.\mathrm{During}\:\mathrm{the}\:\mathrm{time}\:\mathrm{interval}\:\mathrm{from}\:\mathrm{t}=\mathrm{0}\:\mathrm{to}\:\mathrm{t}=\frac{\mathrm{1}}{\mathrm{30}}\:\mathrm{seconds},\: \\ $$$$\mathrm{the}\:\mathrm{average}\:\mathrm{electromotive}\:\mathrm{force}\:\left(\mathrm{e}.\mathrm{m}.\mathrm{f}\right)\:\mathrm{induced}\:\mathrm{in}\:\mathrm{the}\:\mathrm{coil}\:\mathrm{is}: \\ $$$$\left(\mathrm{a}\right)\mathrm{42}.\mathrm{46}\:{V} \\ $$$$\left(\mathrm{b}\right)\mathrm{19}.\mathrm{11}\:{V} \\ $$$$\left(\mathrm{c}\right)\mathrm{127}.\mathrm{39}\:{V} \\ $$$$\left(\mathrm{d}\right)\mathrm{173}.\mathrm{21}\:{V} \\…

Question-215344

Question Number 215344 by universe last updated on 03/Jan/25 Answered by MrGaster last updated on 04/Jan/25 $$\:\mathrm{Let}\:\Sigma\:\mathrm{be}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{of}\:{D}. \\ $$$$\Sigma=\sum_{\mathrm{1}} \cup\sum_{\mathrm{2}} \cup\sum_{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{where} \\ $$$$\sum_{\mathrm{1}}…