Question Number 32351 by abdo imad last updated on 23/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\:\frac{{dt}}{\mathrm{1}+{cos}\theta\:{sint}}\:.\: \\ $$ Answered by sma3l2996 last updated on 25/Mar/18 $${let}\:{x}={tan}\left({t}/\mathrm{2}\right)\Rightarrow{dt}=\frac{\mathrm{2}{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\…
Question Number 32349 by abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{xdx}}{\mathrm{1}+{sinx}}\:. \\ $$ Commented by abdo imad last updated on 24/Mar/18 $${the}\:{ch}.{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\…
Question Number 32342 by abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\int\int_{{D}} \:\:\:\frac{{dxdy}}{\left(\mathrm{4}{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$${D}=\left\{\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:/\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\:{and}\:{y}\:\leqslant\mathrm{2}{x}\:\right\}\:. \\ $$ Terms of Service…
Question Number 32343 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{{dt}}{{x}−{e}^{{it}} }\:\:. \\ $$ Commented by abdo imad last updated on 28/Mar/18 $${let}\:{put}\:{I}\left({x}\right)\:=\:\int_{\mathrm{0}}…
Question Number 163414 by AbdullahIbrahim last updated on 06/Jan/22 $$\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{cosx}}\:\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}}+\sqrt{\boldsymbol{{sinx}}\:\boldsymbol{{cos}}^{\mathrm{3}} \boldsymbol{{x}}}} \\ $$ Answered by Ar Brandon last updated on 06/Jan/22 $${I}=\int\frac{{dx}}{\:\sqrt{\mathrm{cos}{x}\mathrm{sin}^{\mathrm{3}} {x}}+\sqrt{\mathrm{sin}{x}\mathrm{cos}^{\mathrm{3}} {x}}}…
Question Number 32341 by abdo imad last updated on 23/Mar/18 $${let}\:{give}\:\lambda\:{from}\:{R}\:{and}\:\lambda^{\mathrm{2}} \neq\mathrm{1}\:{and} \\ $$$${I}_{{n}} \left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{cos}\left({nt}\right)}{\mathrm{1}−\mathrm{2}\lambda{cost}\:+\lambda^{\mathrm{2}} }{dt}\:\:.{calculate}\:{I}_{{n}} \left(\lambda\right). \\ $$ Commented by abdo imad…
Question Number 32339 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{th}\left(\mathrm{3}{x}\right)\:−{th}\left(\mathrm{2}{x}\right)}{{x}}\:{dx}\:. \\ $$ Commented by abdo imad last updated on 24/Mar/18 $${I}\:={lim}\:_{\xi\rightarrow+\infty} {I}\left(\xi\right)\:\:{with}\:{I}\left(\xi\right)\:=\:\int_{\mathrm{0}}…
Question Number 32340 by abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}^{\mathrm{3}} {t}}{{t}^{\mathrm{2}} }\:{dt}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32338 by abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}\:{dt}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32337 by abdo imad last updated on 23/Mar/18 $$\left.\mathrm{1}\right){calculate}\:\int_{{a}} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} \:−{a}^{\mathrm{2}} }}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} \:−\mathrm{4}}}\:\:. \\ $$ Terms…