Question Number 83008 by mathmax by abdo last updated on 26/Feb/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ch}\left({cosx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 17473 by Arnab Maiti last updated on 06/Jul/17 $$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\mathrm{2a}} \sqrt{\mathrm{2ax}−\mathrm{x}^{\mathrm{2}} }\mathrm{dx}=\frac{\Pi\mathrm{a}^{\mathrm{2}} }{\mathrm{2}} \\ $$ Answered by sma3l2996 last updated on 06/Jul/17 $${A}=\int_{\mathrm{0}}…
Question Number 148546 by mathdanisur last updated on 29/Jul/21 $$\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {{lim}}\:\frac{\sqrt{{x}\:+\:\mathrm{4}}\:-\:\mathrm{2}}{{sinx}}\:=\:? \\ $$ Commented by EDWIN88 last updated on 29/Jul/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}\sqrt{\mathrm{1}+\frac{{x}}{\mathrm{4}}}−\mathrm{2}}{\mathrm{sin}\:{x}}\:= \\ $$$$\:\mathrm{2}×\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\frac{{x}}{\mathrm{4}}}−\mathrm{1}}{\mathrm{sin}\:{x}}\:=…
Question Number 83009 by mathmax by abdo last updated on 26/Feb/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({chx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 17472 by Arnab Maiti last updated on 06/Jul/17 $$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{6}} ^{\mathrm{11}} \frac{\mathrm{dx}}{\:\sqrt{\left(\mathrm{x}−\mathrm{2}\right)\left(\mathrm{x}−\mathrm{3}\right)}}=\mathrm{2ln}\frac{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{2}+\sqrt{\mathrm{3}}} \\ $$ Answered by sma3l2996 last updated on 06/Jul/17 $${I}=\int_{\mathrm{6}} ^{\mathrm{11}} \frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 148541 by gloriousman last updated on 29/Jul/21 Answered by Olaf_Thorendsen last updated on 29/Jul/21 $$\mathrm{The}\:\mathrm{sequence}\:\mathrm{seems}\:\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{sequence} \\ $$$$\mathrm{of}\:\mathrm{rational}\:\mathrm{numbers}\:\mathrm{and}\:\mathrm{the}\:\mathrm{limit} \\ $$$$\mathrm{seems}\:\mathrm{to}\:\mathrm{tend}\:\mathrm{to}\:\mathrm{0}. \\ $$$$\mathrm{We}\:\mathrm{try}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{like}\:: \\ $$$${u}_{{n}}…
Question Number 148540 by Jonathanwaweh last updated on 29/Jul/21 Answered by Olaf_Thorendsen last updated on 29/Jul/21 $$\mathrm{Formule}\:\mathrm{d}'\mathrm{Al}−\mathrm{Kashi}\:\left(\mathrm{generalisation}\right. \\ $$$$\mathrm{de}\:\mathrm{Pythagore}\:\mathrm{dans}\:\mathrm{un}\:\mathrm{triangle} \\ $$$$\left.\mathrm{quelconque}\right)\:: \\ $$$${c}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 148543 by liberty last updated on 29/Jul/21 Answered by Rasheed.Sindhi last updated on 30/Jul/21 $${Let}\:\angle\mathrm{B}=\alpha\:,\:\angle\mathrm{C}=\beta\:, \\ $$$$\bigtriangleup\mathrm{ABC}: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{AC}^{\mathrm{2}} =\mathrm{AB}^{\mathrm{2}} +\mathrm{BC}^{\mathrm{2}} −\mathrm{2}.\mathrm{AB}.\mathrm{BC}.\mathrm{cos}\:\alpha \\…
Question Number 17463 by alex041103 last updated on 06/Jul/17 $${Evaluate}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{{x}^{\mathrm{4}} \left(\mathrm{1}−{x}\right)^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}. \\ $$ Answered by ajfour last updated on 06/Jul/17 $$\frac{\mathrm{22}}{\mathrm{7}}−\pi\:.…
Question Number 148532 by cherokeesay last updated on 28/Jul/21 Answered by mr W last updated on 29/Jul/21 Commented by mr W last updated on 29/Jul/21…