Question Number 31083 by abdo imad last updated on 02/Mar/18 $${calculate}\:{by}\:{two}\:{methods}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dx}\:{dt}}{\mathrm{1}+{x}^{\mathrm{2}} {tan}^{\mathrm{2}} {t}} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{t}\:{cotant}\:{dt}\:. \\ $$$$ \\ $$…
Question Number 31084 by abdo imad last updated on 02/Mar/18 $${find}\:\int\int_{{D}} \:\:\frac{{dxdy}}{\left({x}+{y}\right)^{\mathrm{4}} }\:\:{with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{1},{y}\geqslant\mathrm{1},{x}+{y}\leqslant\mathrm{4}\right\} \\ $$ Commented by abdo imad last updated on 11/Mar/18 $${x}+{y}\:\leqslant\mathrm{4}\:\:{and}\:{y}\geqslant\mathrm{1}\:\Rightarrow−{y}\leqslant−\mathrm{1}\:{but}\:{x}\:\leqslant\mathrm{4}−{y}\:\Rightarrow\mathrm{1}\leqslant{x}\leqslant\mathrm{3}\:{and}…
Question Number 31082 by abdo imad last updated on 02/Mar/18 $${calculate}\:{by}\:{two}\:{methods}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dxdy}}{\left(\mathrm{1}+{y}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} {y}\right)} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\mathrm{1}−{x}^{\mathrm{2}} }{dx}. \\ $$ Terms of…
Question Number 31081 by abdo imad last updated on 02/Mar/18 $${find}\:\:\int_{\mathrm{0}} ^{\infty} {dx}\:\int_{{x}} ^{+\infty} \:{e}^{−{y}^{\mathrm{2}} {dy}} \:\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 31079 by abdo imad last updated on 02/Mar/18 $${calculate}\:\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{0}\leqslant{y}\leqslant\mathrm{2}} \:\:\:{x}^{\mathrm{2}} {y}\:{e}^{{xy}} {dxdxy}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31080 by abdo imad last updated on 02/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{px}} {dx}\:\int_{\mathrm{0}} ^{{a}} \:\:\frac{{cos}\left({xt}\right)}{\:\sqrt{{a}^{\mathrm{2}} \:−{t}^{\mathrm{2}} }}{dt}\:{with}\:{a}>\mathrm{0}\:,{p}>\mathrm{0} \\ $$ Terms of Service Privacy Policy…
Question Number 31077 by abdo imad last updated on 02/Mar/18 $${calculate}\:\int\int_{\mathrm{0}<{x}<\mathrm{1}{and}\:\mathrm{0}<{y}<{x}^{\mathrm{2}} } \:\frac{{y}}{\:\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }}{dxdy}. \\ $$ Commented by abdo imad last updated on 07/Mar/18…
Question Number 31078 by abdo imad last updated on 02/Mar/18 $${find}\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{3}\:{and}\:{x}\leqslant{y}\leqslant\mathrm{4}{x}−{x}^{\mathrm{2}} } \:\:\:\left({x}^{\mathrm{2}} \:+\mathrm{2}{y}\right){dxdy}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31076 by abdo imad last updated on 02/Mar/18 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}} \:\:\:\:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{1}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on 07/Mar/18…
Question Number 96613 by s.ayeni14@yahoo.com last updated on 03/Jun/20 $$\int\mathrm{sec}\theta\mathrm{d}\theta \\ $$ Answered by M±th+et+s last updated on 03/Jun/20 $$\int{sec}\left(\theta\right)\frac{{sec}\left(\theta\right)+{tan}\left(\theta\right)}{{sec}\left(\theta\right)+{tan}\left(\theta\right)}{d}\theta \\ $$$$={ln}\mid{sec}\left(\theta\right)+{tan}\left(\theta\right)\mid+{c} \\ $$$${i}\:{have}\:{more}\:{than}\:\mathrm{9}\:{ways}\:{to}\:{solve}\:{this} \\…