Question Number 201462 by hardmath last updated on 06/Dec/23 $$\mathrm{Find}: \\ $$$$\int_{\mathrm{0}} ^{\:\boldsymbol{\pi}} \:\sqrt{\mathrm{1}\:-\:\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{2}}\:\mathrm{cos}^{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$ Answered by esmaeil last updated on 06/Dec/23…
Question Number 201430 by hardmath last updated on 06/Dec/23 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{2}}{\mathrm{35}}\:+\:\frac{\mathrm{2}}{\mathrm{63}}\:+\:\frac{\mathrm{2}}{\mathrm{99}}\:+\:\frac{\mathrm{2}}{\mathrm{143}}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 06/Dec/23 $$\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{2}} −\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{8}^{\mathrm{2}} −\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{10}^{\mathrm{2}} −\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{12}^{\mathrm{2}}…
Question Number 201463 by hardmath last updated on 06/Dec/23 $$\mathrm{a}\:=\:\mathrm{constant}\:\mathrm{number}: \\ $$$$\mathrm{if}\:\:\:\int\mathrm{x}\:\centerdot\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:-\:\frac{\mathrm{a}}{\mathrm{5}} \\ $$$$\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{2}\right)\:=\:? \\ $$ Answered by mr W last updated on…
Question Number 201456 by Calculusboy last updated on 06/Dec/23 Answered by MathematicalUser2357 last updated on 04/Jan/24 $$? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 201425 by mathlove last updated on 06/Dec/23 $${prove}\:{that} \\ $$$$\frac{\mathrm{1}−{cosA}+{cosB}−{cos}\left({A}+{B}\right)}{\mathrm{1}+{cosA}−{cosB}−{cos}\left({A}+{B}\right)}={tan}\frac{{A}}{\mathrm{2}}\centerdot{cot}\frac{{B}}{\mathrm{2}} \\ $$ Answered by esmaeil last updated on 06/Dec/23 $$\frac{\mathrm{2}{sin}^{\mathrm{2}} \left(\frac{{A}+{B}}{\mathrm{2}}\right)\:−\mathrm{2}{sin}\left(\frac{{B}+{A}}{\mathrm{2}}\right){sin}\left(\frac{{B}−{A}}{\mathrm{2}}\right)}{\mathrm{2}{sin}^{\mathrm{2}} \left(\frac{{B}+{A}}{\mathrm{2}}\right)−\mathrm{2}{sin}\left(\frac{{B}+{A}}{\mathrm{2}}\right){sin}\left(\frac{{A}−{B}}{\mathrm{2}}\right)}= \\…
Question Number 201426 by mathlove last updated on 06/Dec/23 $${cosx}−\sqrt{\mathrm{3}}{sinx}=\mathrm{1} \\ $$$${x}=? \\ $$ Answered by cortano12 last updated on 06/Dec/23 $$\:\:\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{cos}\:\mathrm{x}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{sin}\:\mathrm{x}\right)=\:\mathrm{1} \\ $$$$\:\:\:\:\mathrm{cos}\:\left(\mathrm{x}+\mathrm{60}°\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}=\:\mathrm{cos}\:\mathrm{60}°\: \\…
Question Number 201427 by mathlove last updated on 06/Dec/23 $$\begin{cases}{{sin}\left({x}+{y}\right)={cos}\left({x}−{y}\right)}\\{{tanx}−{tany}=\mathrm{1}}\end{cases} \\ $$$$\left({x},{y}\right)=\left(?,?\right) \\ $$ Answered by Rasheed.Sindhi last updated on 06/Dec/23 $$\begin{cases}{{sin}\left({x}+{y}\right)={cos}\left({x}−{y}\right)…\left({i}\right)}\\{{tanx}−{tany}=\mathrm{1}………\left({ii}\right)}\end{cases} \\ $$$$\left({x},{y}\right)=\left(?,?\right) \\…
Question Number 201452 by tri26112004 last updated on 06/Dec/23 Answered by Calculusboy last updated on 06/Dec/23 $$\int\boldsymbol{{x}}^{−\mathrm{2}} \boldsymbol{{e}}^{−\mathrm{4}\boldsymbol{{x}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{Solution}}:\:\:\boldsymbol{{by}}\:\boldsymbol{{using}}\:\boldsymbol{{IBP}} \\ $$$$\boldsymbol{{let}}\:\boldsymbol{{u}}=\boldsymbol{{e}}^{−\mathrm{4}\boldsymbol{{x}}} \:\:\:\boldsymbol{{du}}=−\mathrm{4}\boldsymbol{{e}}^{−\mathrm{4}\boldsymbol{{x}}} \boldsymbol{{dx}}\:\:\boldsymbol{{dv}}=\boldsymbol{{x}}^{−\mathrm{2}}…
Question Number 201421 by mr W last updated on 06/Dec/23 Commented by mr W last updated on 06/Dec/23 Commented by mr W last updated on…
Question Number 201418 by cortano12 last updated on 06/Dec/23 $$\:\:\:\:\:\:\mathrm{2025}^{\mathrm{2025}} \:=\:\mathrm{x}\:\left(\mathrm{mod}\:\mathrm{17}\:\right) \\ $$ Answered by mr W last updated on 06/Dec/23 $$\mathrm{2025}^{\mathrm{2025}} \:\left({mod}\:\mathrm{17}\right) \\ $$$$=\left(\mathrm{119}×\mathrm{17}+\mathrm{2}\right)^{\mathrm{2025}}…