Question Number 200586 by Calculusboy last updated on 20/Nov/23 Answered by Frix last updated on 21/Nov/23 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{x}}{\mathrm{2}+\mathrm{tan}^{\mathrm{2}} \:{x}}{dx}=\underset{\mathrm{0}} {\overset{\pi} {\int}}{xdx}−\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \:{x}}…
Question Number 200474 by Rupesh123 last updated on 19/Nov/23 Answered by witcher3 last updated on 19/Nov/23 $$\mathrm{erf}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\:\sqrt{\pi}}\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt} \\ $$$$\mathrm{ln}\left(\mathrm{x}+\mathrm{ln}\left(\mathrm{x}\right)\right)=\int_{\mathrm{0}} ^{\mathrm{5}} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}}…
Question Number 200464 by Frix last updated on 19/Nov/23 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{{dx}}{\mathrm{1}+\mathrm{tan}^{\mathrm{2023}} \:{x}}=??????? \\ $$ Answered by som(math1967) last updated on 19/Nov/23 $$\:{I}=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{{cos}^{\mathrm{2023}}…
Question Number 200444 by Calculusboy last updated on 18/Nov/23 Answered by Frix last updated on 19/Nov/23 $$\int\mathrm{e}^{−\mathrm{i}{x}^{\mathrm{2}} } {dx}\:\overset{{t}=\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{4}}} {x}} {=} \\ $$$$=\frac{\sqrt{\mathrm{2}}\left(\mathrm{1}−\mathrm{i}\right)}{\mathrm{2}}\int\mathrm{e}^{−{t}^{\mathrm{2}} } {dt}=\frac{\sqrt{\mathrm{2}\pi}\left(\mathrm{1}−\mathrm{i}\right)}{\mathrm{4}}\int\frac{\mathrm{2e}^{{t}^{\mathrm{3}}…
Question Number 200403 by Anonim_X last updated on 18/Nov/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\left(\boldsymbol{{x}}^{\mathrm{2}} \:+\:\:\mathrm{1}\right)\boldsymbol{{dx}}}{\boldsymbol{{x}}\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}+\mathrm{1}\right)}\:=\:?? \\ $$$$ \\ $$ Answered by cortano12 last updated on 18/Nov/23 $$\:\mathrm{I}\:=\:\int\:\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 200366 by ajfour last updated on 17/Nov/23 Commented by ajfour last updated on 17/Nov/23 $${The}\:{red}\:{circular}\:{arc}\:{length}\:{is}\:{equal} \\ $$$$\:{to}\:{blue}\:{arclength}\:\:{of}\:{parabola}.\:{Find}\: \\ $$$${the}\:{equation}\:{of}\:{parabola}\:{in}\:{the}\:{form}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}={ax}^{\mathrm{2}} +{c}. \\…
Question Number 200253 by Calculusboy last updated on 16/Nov/23 Answered by kapoorshah last updated on 16/Nov/23 $$\mathrm{1} \\ $$ Answered by kapoorshah last updated on…
Question Number 200254 by mnjuly1970 last updated on 16/Nov/23 $$ \\ $$$$\:\:\:\:\:\:{calculate}\:… \\ $$$$\:\:\Omega\:=\:\int_{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\left(\mathrm{tan}\left({x}\right)\right){dx}} ^{\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }\:{dx}} \mathrm{ln}\left(\mathrm{sin}\left({x}\right)\right){dx}=? \\ $$ Answered…
Question Number 200250 by Calculusboy last updated on 16/Nov/23 Answered by Mathspace last updated on 16/Nov/23 $$\int_{\mathrm{0}} ^{{x}} {sin}\left({x}+{t}\right){dt} \\ $$$$=\left[{cos}\left({x}+{t}\right)\right]_{{t}=\mathrm{0}} ^{{t}={x}} ={cos}\left(\mathrm{2}{x}\right)−{cosx} \\ $$$$\Rightarrow\frac{{d}}{{dx}}\left(\int_{\mathrm{0}}…
Question Number 200299 by Calculusboy last updated on 16/Nov/23 Answered by witcher3 last updated on 17/Nov/23 $$\mathrm{x}\rightarrow\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\Omega=\int_{\infty} ^{\mathrm{0}} −\frac{\frac{\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)}{\mathrm{x}}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{4}} }.\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{x}^{\mathrm{2}}…