Question Number 31090 by abdo imad last updated on 02/Mar/18 $${find}\:\int\int_{\mathrm{1}\leqslant{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{4}\:{and}\:{y}\geqslant\mathrm{0}} \:\:\:\frac{{dxdy}}{\:\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on…
Question Number 31091 by abdo imad last updated on 02/Mar/18 $${let}\:\:−\mathrm{1}<{t}<\mathrm{1}\:{find}\:{f}\left({t}\right)=\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{ln}\left(\mathrm{1}+{tcosx}\right)}{{cosx}}{dx} \\ $$ Commented by abdo imad last updated on 06/Mar/18 $${we}\:{have}\:{f}^{'} \left({t}\right)=\int_{\mathrm{0}}…
Question Number 31087 by abdo imad last updated on 02/Mar/18 $${find}\:\int\int\int_{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} \:<\mathrm{4}} \:\:\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} \right){dxdydz}. \\ $$ Terms of Service Privacy Policy…
Question Number 31088 by abdo imad last updated on 02/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{dx}\:\int_{\mathrm{0}} ^{\mathrm{1}−{x}} \:\:{e}^{\frac{{y}−{x}}{{y}+{x}}} \:{dy}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31086 by abdo imad last updated on 02/Mar/18 $${find}\:\int\int_{{D}} \left({x}^{\mathrm{4}} \:−{y}^{\mathrm{4}} \right){dxdy}\:{with} \\ $$$${D}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{1}<{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} <\mathrm{2}\:,\mathrm{1}<{xy}<\mathrm{2}\:,{x}>\mathrm{0},{y}>\mathrm{0}\right\} \\ $$ Terms of Service Privacy…
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