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Category: Integration

can-some-one-find-the-exact-value-of-n-0-1-n-2-

Question Number 206890 by mathzup last updated on 29/Apr/24 $${can}\:{some}\:{one}\:{find}\:{the}\:{exact}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\left({n}!\right)^{\mathrm{2}} } \\ $$ Commented by Frix last updated on 30/Apr/24 $$\mathrm{This}\:\mathrm{is}\:\mathrm{a}\:\mathrm{Modified}\:\mathrm{Bressel}\:\mathrm{Function}\:\mathrm{of}\:\mathrm{the}…

c-a-0-a-1-1-f-x-2-dx-2-b-0-b-1-1-f-x-2-dx-2-c-L-1-2-L-2-2-

Question Number 206830 by Fabricista15 last updated on 27/Apr/24 $${c}\:=\:\sqrt{\left(\int_{{a}_{\mathrm{0}} } ^{{a}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} +\left(\int_{{b}_{\mathrm{0}} } ^{{b}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} } \\ $$$${c}\:=\:\sqrt{{L}_{\mathrm{1}} ^{\mathrm{2}}…

xdx-x-4-please-

Question Number 206721 by ajfour last updated on 23/Apr/24 $$\int\frac{{xdx}}{{x}+\mathrm{4}}=?\:\:\:\:\:\:\:{please} \\ $$ Answered by A5T last updated on 23/Apr/24 $$\frac{{x}}{{x}+\mathrm{4}}=\frac{{x}+\mathrm{4}−\mathrm{4}}{{x}+\mathrm{4}}=\mathrm{1}−\frac{\mathrm{4}}{{x}+\mathrm{4}} \\ $$$$\Rightarrow\int\frac{{x}}{{x}+\mathrm{4}}{dx}=\int\mathrm{1}{dx}−\mathrm{4}\int\frac{\mathrm{1}}{{x}+\mathrm{4}}{dx} \\ $$$$={x}−\mathrm{4}{ln}\mid{x}+\mathrm{4}\mid+{c} \\…

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 $$\mathrm{The}\:\mathrm{calculation}\:\mathrm{was}\:\mathrm{aborted}\:\mathrm{because}\:\mathrm{it}\:\mathrm{took}\:\mathrm{too} \\ $$$$\mathrm{long}.\:\mathrm{Please}\:\mathrm{make}\:\mathrm{sure}\:\mathrm{that}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{incorrect},\:\mathrm{or} \\ $$$$\mathrm{try}\:\mathrm{tosimplify}\:\mathrm{your}\:\mathrm{query}.\:{Have}\:{you}\:{tried}\:{using}\:{the} \\ $$$${option}\:{to}\:{simplify}\:{expressions}??? \\ $$…