Question Number 221049 by Nicholas666 last updated on 23/May/25 $$ \\ $$$$\:\:\:\:\int\:\:\frac{\mathrm{cos}\:{x}}{\left({x}\:+\:\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{2}\left(\mathrm{1}\:−\:\mathrm{sin}\:{x}\right)^{\mathrm{2}} }{\left({x}\:+\:\mathrm{cos}\:{x}\right)^{\mathrm{3}} }\:\:\mathrm{d}{x}\: \\ $$$$\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221048 by fantastic last updated on 23/May/25 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\mathrm{cosec}\:\left({x}−\frac{\pi}{\mathrm{3}}\right)\mathrm{cosec}\:\left({x}−\frac{\pi}{\mathrm{6}}\right){dx}\: \\ $$ Answered by vnm last updated on 24/May/25 $$ \\ $$$$\mathrm{the}\:\mathrm{integral}\:\mathrm{diverges},\:\mathrm{but}\:\mathrm{it}'\mathrm{s} \\…
Question Number 221057 by fantastic last updated on 23/May/25 Commented by fantastic last updated on 23/May/25 $${Please}\:{find}\:{the}\:{area}\:{of}\:{shaded}\:{region}\:{using}\:{calculus} \\ $$ Answered by mr W last updated…
Question Number 221008 by MrGaster last updated on 22/May/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 220963 by fantastic last updated on 21/May/25 $${Let}\:{f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R}\:{be}\:{defined}\:{by}\:{f}\left({x},{y}\right)=\left\{\frac{{y}}{\underset{\:\:\mathrm{1},\:{y}=\mathrm{0}} {\mathrm{sin}\:{y}}},\:{y}\neq\mathrm{0}\right. \\ $$$${Then}\:{the}\:{integral}\:\frac{\mathrm{1}}{\pi^{\mathrm{2}} }\underset{{x}=\mathrm{0}} {\overset{\mathrm{1}} {\int}}\underset{{y}=\mathrm{sin}^{−\mathrm{1}} {x}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{f}\left({x},{y}\right){dy}\:{dx}\:{correct}\:{upto}\:{three}\:{decimal}\:{places},{is}… \\ $$ Answered by MrGaster…
Question Number 220948 by fantastic last updated on 21/May/25 $$\int\:{x}^{\mathrm{2}} \sqrt{\mathrm{5}−{x}^{\mathrm{6}} }{dx} \\ $$ Answered by SdC355 last updated on 21/May/25 $${x}^{\mathrm{3}} ={u} \\ $$$$\frac{\mathrm{d}{u}}{\mathrm{d}{x}}=\mathrm{3}{x}^{\mathrm{2}}…
Question Number 220950 by Nicholas666 last updated on 21/May/25 $$ \\ $$$$\:\:\:\:\int_{\:\mathrm{0}} ^{\:\pi} \int_{\:\mathrm{0}} ^{\:\mathrm{1}} \int_{\:\mathrm{0}} ^{\:\:\pi} \:\mathrm{sin}^{\:\mathrm{2}} \:{x}\:+\:{y}\:\mathrm{sin}\:{z}\:{dxdydz}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\pi\:\left(\mathrm{2}\:+\:\pi\right)\:\:\:\:\:\: \\ $$$$ \\ $$ Answered by…
Question Number 220848 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\mathrm{2}}\:\sqrt{\frac{\left(\mathrm{2}\:−\:\mathrm{6}{x}\:+\:\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{2}} +\:\mathrm{4}\left(\mathrm{2}{x}\:−\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{x}^{\mathrm{3}} \right)}{\mathrm{2}{x}\:−\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{x}^{\mathrm{3}} }}\:{dx}\:\:\:\:\:\:\: \\ $$$$ \\ $$ Commented…
Question Number 220850 by fantastic last updated on 20/May/25 $$\int\sqrt{\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}}.\frac{\mathrm{1}}{{x}+\mathrm{3}}{dx} \\ $$ Commented by Frix last updated on 20/May/25 $$\mathrm{Question}\:\mathrm{219193} \\ $$$$\mathrm{Why}\:\mathrm{you}\:\mathrm{ask}\:\mathrm{again}? \\ $$ Answered…
Question Number 220842 by mnjuly1970 last updated on 20/May/25 $$ \\ $$$$\:\:\:\:\:\:\mathrm{J}=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{t}} {u}_{\pi} \left({t}\right){cos}\left({t}\right){dt}=? \\ $$$$ \\ $$$$\:{note}:\:\:{u}_{{c}} \left({t}\right)=\:\begin{cases}{\:\mathrm{0}\:\:\:\:\:\:\:\:{t}<{c}}\\{\:\mathrm{1}\:\:\:\:\:\:\:\:\:{t}>{c}\:\:}\end{cases}\:\:;\:\:\:\:{c}\geqslant\mathrm{0} \\ $$ Commented by…