Question Number 93958 by mashallah last updated on 16/May/20 $$\int\frac{\mathrm{sinx}−\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}= \\ $$ Commented by mathmax by abdo last updated on 17/May/20 $${I}\:=\int\:\frac{{sinx}−{cosx}}{{sinx}\:+{cosx}}{dx}\:\Rightarrow{I}\:=\int\frac{{tanx}−\mathrm{1}}{{tanx}\:+\mathrm{1}}{dx}\:=_{{tanx}\:={t}} \\ $$$$=\int\frac{{t}−\mathrm{1}}{{t}+\mathrm{1}}×\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }\:=\int\:\:\:\:\frac{{t}−\mathrm{1}}{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{2}}…
Question Number 93941 by Ar Brandon last updated on 16/May/20 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}\:} \:\mathrm{is}\:\mathrm{of}\:\mathrm{Reimann}\:\mathrm{within} \\ $$$$\mathrm{x}\in\left[\mathrm{1};\mathrm{5}\right]\:\mathrm{hence}\:\mathrm{calculate}\:\int_{\mathrm{1}} ^{\mathrm{5}} \mathrm{e}^{\mathrm{x}} \mathrm{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 93937 by seedhamaieng@gmail.com last updated on 16/May/20 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{tan}\:{x}}}{dx}=? \\ $$ Commented by i jagooll last updated on 16/May/20 $$\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\sqrt{\mathrm{tan}\:\mathrm{x}}}\:\mathrm{dx}\:= \\ $$$$\int\:\frac{\mathrm{du}}{\left(\mathrm{1}+\mathrm{u}^{\mathrm{2}}…
Question Number 93906 by abdomathmax last updated on 16/May/20 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{cosx}} }{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 93907 by abdomathmax last updated on 16/May/20 $$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {x}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{{n}} } \\ $$$${n}\:{integr}\:{natural} \\ $$ Commented…
Question Number 93904 by i jagooll last updated on 16/May/20 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\left({e}^{−{ax}} −{e}^{−{bx}} \right)\:{dx}\: \\ $$ Answered by i jagooll last updated on 16/May/20…
Question Number 93898 by mathmax by abdo last updated on 16/May/20 $${let}\:{f}\left({x}\right)=\mathrm{2}\sqrt{\mathrm{3}−{x}}\:{and}\:{g}\left({x}\right)\:={x}^{\mathrm{2}} −\mathrm{2}{x}\:+\mathrm{5} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{fog}\left({x}\right)\:{and}\:{determine}\:{D}_{{fog}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int\:{fog}\left({x}\right){dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int\:\frac{{f}^{−\mathrm{1}} \left({x}\right)}{{f}\left({x}\right)}{dx}\:\:{and}\:\:\int\:\frac{{f}^{−\mathrm{1}} {og}\left({x}\right)}{{fog}\left({x}\right)}{dx} \\ $$ Commented by…
Question Number 93873 by mathmax by abdo last updated on 15/May/20 $${find}\:\int_{−\infty} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 93869 by i jagooll last updated on 15/May/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:? \\ $$ Commented by i jagooll last updated on 15/May/20 Commented by Tony…
Question Number 93860 by Ar Brandon last updated on 15/May/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{progression}\:\left(\mathrm{I}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{where}\:\mathrm{I}_{\mathrm{n}} \:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{sin}\left(\pi\mathrm{t}\right)}{\mathrm{t}+\mathrm{n}}\mathrm{dt} \\ $$$$\mathrm{1}\backslash\:\mathrm{Show}\:\mathrm{that}:\:\forall\mathrm{n}\geqslant\mathrm{0},\:\mathrm{0}\leqslant\mathrm{I}_{\mathrm{n}+\mathrm{1}} \leqslant\mathrm{I}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{deduce}\:\mathrm{that}\:\mathrm{the}\: \\ $$$$\mathrm{series}\:\mathrm{is}\:\mathrm{convergent}. \\ $$$$\mathrm{2}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{0}\leqslant\mathrm{I}_{\mathrm{n}} \leqslant\mathrm{ln}\left(\frac{\mathrm{n}+\mathrm{1}}{\mathrm{n}}\right)\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{the}\:\mathrm{limit}…