Question Number 59185 by maxmathsup by imad last updated on 09/May/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}}{{sinx}}{dx} \\ $$$${let}\:{f}\left({x}\right)\:={sinx}\:\Rightarrow{f}\left({x}\right)\:={f}\left(\mathrm{0}\right)\:+{xf}^{'} \left(\mathrm{0}\right)\:+\frac{{x}^{\mathrm{2}} }{\mathrm{2}}{f}^{\left(\mathrm{2}\right)} \left(\mathrm{0}\right)+\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}{f}^{\left(\mathrm{3}\right)} \left(\mathrm{0}\right)\:+{o}\left({x}^{\mathrm{4}} \right) \\ $$$${but}\:{f}\left(\mathrm{0}\right)\:=\mathrm{0}\:\:\:{f}^{'} \left({x}\right)\:={cosx}\:\Rightarrow{f}^{'}…
Question Number 59183 by maxmathsup by imad last updated on 05/May/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\mathrm{1}+{ix}\right)}{\mathrm{2}+{x}^{\mathrm{2}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 59175 by maxmathsup by imad last updated on 05/May/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}−{cos}\left({x}\right)}{{x}^{\mathrm{2}} }{dx}\: \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 59174 by maxmathsup by imad last updated on 05/May/19 $${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{2}\right]^{\mathrm{2}} } \:\:\:\:\left({x}+\mathrm{1}−\sqrt{{y}}\right)\left({y}+\mathrm{1}−\sqrt{{x}}\right){dxdy}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 59172 by maxmathsup by imad last updated on 05/May/19 $${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:\:\left({x}+{y}\right){ln}\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){dxdy}\: \\ $$ Commented by maxmathsup by imad last updated…
Question Number 59169 by maxmathsup by imad last updated on 05/May/19 $${calculate}\:{A}_{{n}} =\int\int_{\left[\frac{\mathrm{1}}{{n}},{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:{e}^{−{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} } \sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}{y}^{\mathrm{2}} }{dxdy} \\ $$$${and}\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$…
Question Number 59168 by maxmathsup by imad last updated on 05/May/19 $${calculate}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}} \:+\mathrm{3}}{\:\sqrt{\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}}\:{dx} \\ $$ Answered by ajfour last updated on 05/May/19 $$\frac{\mathrm{I}}{\mathrm{2}}=\int_{\mathrm{0}}…
Question Number 59167 by maxmathsup by imad last updated on 05/May/19 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{n}^{\mathrm{2}} \:+\mathrm{1}}{{n}^{\mathrm{3}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 59165 by maxmathsup by imad last updated on 05/May/19 $${let}\:{D}\:=\left\{\:\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}>\mathrm{0}\:,{y}>\mathrm{0}\:\:{and}\:\:{x}+{y}\:\leqslant\mathrm{2}\:\right\} \\ $$$${calculate}\:\int\int_{{D}} \:\left({x}+{y}\:−\sqrt{{x}+{y}}\right){dxdy}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 59163 by maxmathsup by imad last updated on 05/May/19 $$\left.{calculate}\:{A}_{{n}} =\int\int_{{W}_{{n}} } \:\:\:\frac{\mathrm{1}−\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }}{\mathrm{1}+\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }}\:{dxdy}\:\:\:{with}\:{W}_{{n}} \:=\right]\frac{\mathrm{1}}{{n}},{n}\left[^{\mathrm{2}} \right. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\…