Question Number 27271 by GANGADHARSETHI last updated on 04/Jan/18 $$\boldsymbol{{P}}{roof}\: \\ $$$$\int\frac{\mathrm{1}}{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}\:=\frac{\mathrm{1}}{\mathrm{2}{a}}{ln}\mid\frac{{a}+{x}}{{a}−{x}}\mid+{c} \\ $$ Answered by sma3l2996 last updated on 04/Jan/18 $$\int\frac{{dx}}{{a}^{\mathrm{2}} −{x}^{\mathrm{2}}…
Question Number 92805 by niroj last updated on 09/May/20 $$\:\mathrm{Evaluate}: \\ $$$$\:\int_{\boldsymbol{\mathrm{R}}} \int\:\frac{\boldsymbol{\mathrm{xy}}}{\:\sqrt{\mathrm{1}−\boldsymbol{\mathrm{y}}^{\mathrm{2}} }}\:\boldsymbol{\mathrm{dx}}\:\boldsymbol{\mathrm{dy}}\:\mathrm{where}\:\mathrm{the}\:\mathrm{region}\:\mathrm{of}\:\mathrm{integration}\:\mathrm{is}\:\mathrm{the} \\ $$$$\:\mathrm{positive}\:\mathrm{quadrant}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{1}. \\ $$$$ \\ $$ Answered by mr…
Question Number 92804 by niroj last updated on 09/May/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{differential}\:\mathrm{equations}: \\ $$$$\:\left(\mathrm{i}\right).\:\mathrm{e}^{\mathrm{x}−\mathrm{y}} \:\mathrm{dx}\:+\mathrm{e}^{\mathrm{y}−\mathrm{x}} \:\mathrm{dy}=\mathrm{0} \\ $$$$\:\:\left(\mathrm{ii}\right).\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\sqrt{\mathrm{y}−\mathrm{x}} \\ $$$$\:\left(\mathrm{iii}\right).\:\frac{\mathrm{dy}}{\mathrm{dx}}=\:\frac{\mathrm{3xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{3x}^{\mathrm{2}} } \\ $$$$ \\ $$ Commented…
Question Number 158333 by amin96 last updated on 02/Nov/21 $$\int_{\left(\mathrm{1};\pi\right)} ^{\left(\mathrm{2};\pi\right)} \left(\mathrm{1}−\frac{\boldsymbol{\mathrm{y}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\right)\right)\boldsymbol{\mathrm{dx}}+\left(\boldsymbol{\mathrm{sin}}\left(\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\right)+\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\right)\right)\boldsymbol{\mathrm{dy}}=? \\ $$$$\boldsymbol{\mathrm{OY}}\:\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{road}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{doesn}}'\boldsymbol{\mathrm{t}}\:\boldsymbol{\mathrm{cut}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{arrow}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92801 by niroj last updated on 09/May/20 $$\boldsymbol{\mathrm{Integrate}}\:\boldsymbol{\mathrm{following}}\:: \\ $$$$\:\:\left(\boldsymbol{\mathrm{i}}\right).\int\:\frac{\:\:\mathrm{dx}}{\mathrm{sin}\:\mathrm{x}\left(\:\mathrm{3}+\mathrm{2cos}\:\mathrm{x}\right)} \\ $$$$\:\:\left(\boldsymbol{\mathrm{ii}}\right).\int\sqrt{\frac{\mathrm{sin}\left(\mathrm{x}−\alpha\right)}{\mathrm{sin}\left(\mathrm{x}+\alpha\right)}}\:\:\mathrm{dx}\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92799 by Ar Brandon last updated on 09/May/20 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{x}\rightarrow\mathrm{x}^{\mathrm{3}} \:\mathrm{is} \\ $$$$\mathrm{of}\:\mathrm{Riemann}\:\mathrm{within}\:\mathrm{the}\:\mathrm{interval}\:\left[−\mathrm{1},\mathrm{2}\right] \\ $$$$\mathrm{then}\:\mathrm{calculate}\:\int_{−\mathrm{1}} ^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \mathrm{dx} \\ $$ Commented by mathmax by…
Question Number 92795 by niroj last updated on 09/May/20 $$\boldsymbol{\mathrm{Define}}\:\boldsymbol{\mathrm{Clairaut}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{equation}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{solve}} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{px}}\:+\sqrt{\boldsymbol{\mathrm{a}}^{\mathrm{2}} \boldsymbol{\mathrm{p}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92790 by M±th+et+s last updated on 09/May/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\pi}{\mathrm{4}}−{tan}^{−\mathrm{1}} \left({x}\right)\right)\frac{{dx}}{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158320 by mnjuly1970 last updated on 02/Nov/21 $$ \\ $$$$\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\mathrm{H}_{\:{n}} .\:\mathrm{F}_{{n}} }{\mathrm{2}^{\:{n}} }\:\:=\:{ln}\left(\mathrm{4}\right)\:+\:\frac{\mathrm{12}}{\:\sqrt{\mathrm{5}}}\:{ln}\left(\:\varphi\:\right) \\ $$$$\:\:\:\:\:\varphi\::\:\:\:\mathrm{Golden}\:\:\mathrm{ratio} \\ $$$$\:\:\:\:\:\:\mathrm{F}_{\:{n}}…
Question Number 92772 by Power last updated on 09/May/20 Commented by mathmax by abdo last updated on 09/May/20 $${A}\:=\int_{\mathrm{0}} ^{\mathrm{6}} \:\left[{x}\right]\:{sin}\left(\frac{\pi{x}}{\mathrm{6}}\right){dx}\:\Rightarrow\:{A}\:=\sum_{{k}=\mathrm{0}} ^{\mathrm{5}} \:\int_{{k}} ^{{k}+\mathrm{1}} \:{k}\:{sin}\left(\frac{\pi{x}}{\mathrm{6}}\right){dx}…