Question Number 136481 by BHOOPENDRA last updated on 22/Mar/21 $$\int_{\mathrm{0}} ^{\frac{\mathrm{50}\pi}{\mathrm{3}}} \mid{sinx}\mid{dx} \\ $$ Answered by MJS_new last updated on 22/Mar/21 $$\underset{\mathrm{0}} {\overset{\mathrm{50}\pi/\mathrm{3}} {\int}}\mid\mathrm{sin}\:{x}\mid{dx}=\mathrm{33}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}}…
Question Number 5410 by FilupSmith last updated on 14/May/16 Commented by FilupSmith last updated on 14/May/16 $$\mathrm{An}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{sides}\:\mathrm{of} \\ $$$$\mathrm{length}\:{L},\:\mathrm{contains}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{with} \\ $$$$\mathrm{lengths}\:{a}\:\mathrm{and}\:{b}. \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{size}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}?…
Question Number 136482 by rexford last updated on 22/Mar/21 $${f}\left({x}\right)=\int_{−\Pi/\mathrm{4}} ^{\Pi\int/\mathrm{4}} {e}^{{xtant}} {dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136476 by Ar Brandon last updated on 22/Mar/21 $$\left(\mathrm{a}\right)\:\mathrm{Let}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\left(\mathrm{x}−\frac{\alpha}{\mathrm{x}}\right)^{\mathrm{2}} } \mathrm{dx} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{it}\:\mathrm{is}\:\mathrm{legitimate}\:\mathrm{to}\:\mathrm{take}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{I}\left(\alpha\right)\:\mathrm{and}\:\mathrm{also}\:\mathrm{I}'\left(\alpha\right)= \\ $$$$\mathrm{0}.\:\mathrm{Then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\left(\alpha\right)=\frac{\sqrt{\pi}}{\mathrm{2}}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Use}\:\left(\mathrm{a}\right)\:\mathrm{to}\:\mathrm{prove}…
Question Number 5406 by 1771727373 last updated on 14/May/16 $$\int_{−\infty} ^{\infty} \:{e}^{{x}} {dx}=? \\ $$ Commented by FilupSmith last updated on 14/May/16 $${S}=\underset{{k}\rightarrow\infty} {\mathrm{lim}}\:\underset{−{k}} {\overset{{k}}…
Question Number 5405 by sanusihammed last updated on 14/May/16 $${The}\:{angle}\:{of}\:{elevation}\:{of}\:{point}\:{A}\:{and}\:{B}\:{from}\:{P}\:{are}\:\alpha\:{and}\:\beta\: \\ $$$${respectively}.\:{The}\:{bearing}\:{of}\:{A}\:{and}\:{B}\:{from}\:{P}\:{are}\:{S}\mathrm{20}°{W}\:{and} \\ $$$${S}\mathrm{40}°{E}\:{and}\:{their}\:{distance}\:{from}\:{P}\:\:{measured}\:{on}\:{the}\:{map}\:{are} \\ $$$$\mathrm{3}{cm}\:{and}\:\mathrm{1}{cm}\:{respetively}.\:{A}\:{is}\:{higher}\:{than}\:{B}.\:{Prove}\:{that}\:{the}\: \\ $$$${elevation}\:{of}\:{A}\:{from}\:{B}\:{is} \\ $$$$ \\ $$$$\frac{{tan}^{−\mathrm{1}} \left[\mathrm{3}{tan}\alpha\:−\:{tan}\beta\right]}{\:\sqrt{\mathrm{7}}\:} \\ $$$$…
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Question Number 136475 by EDWIN88 last updated on 22/Mar/21 Commented by EDWIN88 last updated on 22/Mar/21 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{fact}\:\mathrm{that}\:\mathrm{csc}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{x}}{\mathrm{6}}+\frac{\mathrm{7x}^{\mathrm{3}} }{\mathrm{360}}+\frac{\mathrm{31x}^{\mathrm{5}} }{\mathrm{15120}}+…\:\mathrm{for}\:\mid\mathrm{x}\mid\:<\:\pi\:\mathrm{to} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{for} \\ $$$$\mathrm{2}\:\mathrm{csc}\:\left(\mathrm{2x}\right)\:\left[\:\mathrm{for}\:\mid\mathrm{x}\mid\:<\:\frac{\pi}{\mathrm{2}}\:\mathrm{and}\:\mathrm{thus}\:\mathrm{for}\:\mathrm{ln}\:\left(\mathrm{tan}\:\mathrm{x}\right).\right. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{ln}\:\mid\mathrm{x}\mid\:+\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 5398 by FilupSmith last updated on 13/May/16 $$\mathrm{If}\:\mathrm{we}\:\mathrm{have}\:\mathrm{an}\:{n}−\mathrm{dimensional}\:\mathrm{cube}. \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{we}\:\mathrm{find}\:\mathrm{its}\:'{volume}'? \\ $$ Commented by Rasheed Soomro last updated on 13/May/16 $$\mathrm{Suppose}\:\mathrm{s}\:\:\mathrm{is}\:\mathrm{measure}\:\mathrm{of}\:\mathrm{side}\:\mathrm{of}\: \\ $$$$\mathrm{n}-\mathrm{dimensional}\:\mathrm{cube}.…