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Author: Tinku Tara

Question-206674

Question Number 206674 by 073 last updated on 22/Apr/24 Answered by Frix last updated on 22/Apr/24 $$\Gamma\left({x}\right)=\underset{\mathrm{0}} {\overset{\infty} {\int}}{t}^{{x}−\mathrm{1}} \mathrm{e}^{−{t}} {dt} \\ $$$$\frac{{d}\Gamma\left({x}\right)}{{dx}}=\Gamma'\left({x}\right)=\underset{\mathrm{0}} {\overset{\infty} {\int}}{t}^{{x}−\mathrm{1}}…

Let-f-x-x-x-10-and-let-A-be-the-region-enclosed-within-the-following-points-2-7-8-7-2-4-8-4-what-is-the-average-arc-length-of-a-f-x-inside-A-a-R-

Question Number 206645 by Red1ight last updated on 21/Apr/24 $$\mathrm{Let}\:{f}\left({x}\right)={x}\left({x}−\mathrm{10}\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{A}\:\mathrm{be}\:\mathrm{the}\:\mathrm{region}\:\mathrm{enclosed}\:\mathrm{within} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{points} \\ $$$$\left(\mathrm{2},\mathrm{7}\right),\left(\mathrm{8},\mathrm{7}\right),\left(\mathrm{2},\mathrm{4}\right),\left(\mathrm{8},\mathrm{4}\right) \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{average}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\centerdot{f}\left({x}\right) \\ $$$$\mathrm{inside}\:\mathrm{A},{a}\in\mathbb{R}^{−} \\ $$ Commented by mr…

Question-206642

Question Number 206642 by universe last updated on 21/Apr/24 Answered by MathematicalUser2357 last updated on 26/Apr/24 $$\mathrm{The}\:\mathrm{calculation}\:\mathrm{was}\:\mathrm{aborted}\:\mathrm{because}\:\mathrm{it}\:\mathrm{took}\:\mathrm{too} \\ $$$$\mathrm{long}.\:\mathrm{Please}\:\mathrm{make}\:\mathrm{sure}\:\mathrm{that}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{incorrect},\:\mathrm{or} \\ $$$$\mathrm{try}\:\mathrm{tosimplify}\:\mathrm{your}\:\mathrm{query}.\:{Have}\:{you}\:{tried}\:{using}\:{the} \\ $$$${option}\:{to}\:{simplify}\:{expressions}??? \\ $$…

Question-206637

Question Number 206637 by jshfnahdj last updated on 21/Apr/24 Answered by Frix last updated on 21/Apr/24 $${x}^{{y}} \:\mathrm{with}\:{x},\:{y}\:\in\mathbb{C} \\ $$$$\mathrm{We}\:\mathrm{need}\:{x}={r}\mathrm{e}^{\mathrm{i}\theta} \:\mathrm{and}\:{y}={a}+{b}\mathrm{i}\:\Rightarrow \\ $$$${x}^{{y}} =\left({r}\mathrm{e}^{\mathrm{i}\theta} \right)^{{a}+{b}\mathrm{i}}…

Question-206639

Question Number 206639 by mathlove last updated on 21/Apr/24 Commented by Frix last updated on 21/Apr/24 $$=\underset{\frac{\pi}{\mathrm{12}}} {\overset{\frac{\pi}{\mathrm{11}}} {\int}}\left(\frac{\sqrt{{s}}}{\mathrm{2}\left(\sqrt{{c}}+\sqrt{{s}}\right)}−\frac{\sqrt{{cs}}}{{c}+\sqrt{{s}}\left(\sqrt{{c}}+\mathrm{1}\right)}+\frac{\left(\sqrt{{c}}−\mathrm{1}\right){s}+\sqrt{{cs}}}{\mathrm{2}\left(\left(\sqrt{{s}}+\mathrm{1}\right){c}+\left(\sqrt{{c}}+\mathrm{1}\right){s}\right)}\right){dx} \\ $$$$\mathrm{With}\:{c}=\mathrm{cos}\:{x}\:\wedge{s}=\mathrm{sin}\:{x} \\ $$$$\mathrm{I}\:\mathrm{doubt}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}. \\ $$…