Question Number 143087 by bramlexs22 last updated on 10/Jun/21 Answered by Ar Brandon last updated on 10/Jun/21 $$\mathrm{x}=\mathrm{sec}\vartheta \\ $$$$\mathrm{I}=\int_{\frac{\mathrm{2}\pi}{\mathrm{3}}} ^{\frac{\mathrm{5}\pi}{\mathrm{6}}} \frac{\mathrm{sec}\vartheta\mathrm{tan}\vartheta}{\mathrm{sec}\vartheta\sqrt{\mathrm{sec}^{\mathrm{2}} \vartheta−\mathrm{1}}}\mathrm{d}\vartheta=\int_{\frac{\mathrm{2}\pi}{\mathrm{3}}} ^{\frac{\mathrm{5}\pi}{\mathrm{6}}} \frac{\mathrm{tan}\vartheta}{\:\sqrt{\mathrm{tan}^{\mathrm{2}}…
Question Number 12013 by tawa last updated on 09/Apr/17 $$\mathrm{The}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{is},\:\mathrm{7x}\:+\:\mathrm{3}\:\:\mathrm{and}\:\mathrm{it}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\:\mathrm{4}\right), \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point} \\ $$ Answered by ajfour last updated on 09/Apr/17 $$\frac{{dy}}{{dx}}=\mathrm{7}{x}+\mathrm{3} \\ $$$$\int{dy}=\int\left(\mathrm{7}{x}+\mathrm{3}\right){dx} \\…
Question Number 143086 by mnjuly1970 last updated on 09/Jun/21 $$ \\ $$$$\:\:{Evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{{ln}\left({tan}\left({x}\right)\right).{sin}^{\pi^{{e}} } \left(\mathrm{2}{x}\right)}{\left({sin}^{\pi^{{e}} } \left({x}\right)+{cos}^{\pi^{{e}} } \left({x}\right)\right)^{\mathrm{2}} }{dx} \\ $$$$…
Question Number 77549 by BK last updated on 07/Jan/20 Commented by abdomathmax last updated on 08/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dz}}{\mathrm{1}−{xyz}}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sum_{{n}=\mathrm{0}} ^{\infty} {x}^{{n}} {y}^{{n}} \:{z}^{{n}}…
Question Number 143081 by Mathspace last updated on 09/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} {xe}^{−{x}^{\mathrm{2}} } {arctanx}\:{dx} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 143080 by Mathspace last updated on 09/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 143083 by Mathspace last updated on 09/Jun/21 $${calculate}\:\Psi\left({a},{b}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{ax}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$${with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Answered by Olaf_Thorendsen last…
Question Number 143082 by Mathspace last updated on 09/Jun/21 $${calculate}\:{f}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{ax}^{\mathrm{2}} } }{{x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} }{dx} \\ $$$${with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Answered by Dwaipayan Shikari last…
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Question Number 12008 by tawa last updated on 09/Apr/17 Commented by chux last updated on 09/Apr/17 $$\mathrm{which}\:\mathrm{country}\:\mathrm{do}\:\mathrm{you}\:\mathrm{come}\:\mathrm{from}\:\mathrm{tawa} \\ $$ Answered by ajfour last updated on…