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Category: Integration

Evaluate-using-cauchy-s-integral-c-e-ipi-z-2-4-2-z-1-2-dz-where-c-is-a-circle-with-z-i-3-5-help-please-

Question Number 85260 by Umar last updated on 20/Mar/20 $$\mathrm{Evaluate}\:\mathrm{using}\:\mathrm{cauchy}'\mathrm{s}\:\mathrm{integral}\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{c}} \:\frac{\mathrm{e}^{\mathrm{i}\pi} }{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{2}} \left(\mathrm{z}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dz} \\ $$$$\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mid\mathrm{z}−\mathrm{i}\mid=\mathrm{3}.\mathrm{5} \\ $$$$ \\ $$$$\mathrm{help}\:\mathrm{please} \\ $$…

0-1-sin-ln-x-ln-x-dx-

Question Number 85256 by john santu last updated on 20/Mar/20 $$\int\underset{\mathrm{0}} {\overset{\:\mathrm{1}} {\:}}\:\frac{\mathrm{sin}\:\left(\mathrm{ln}\:\mathrm{x}\right)}{\mathrm{ln}\:\left(\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$ Commented by john santu last updated on 20/Mar/20 $$\mathrm{sin}\:\left(\mathrm{z}\right)\:=\:\frac{\mathrm{e}^{\mathrm{iz}\:} −\mathrm{e}^{−\mathrm{iz}}…

find-f-x-if-f-x-f-x-2-2x-1-

Question Number 85236 by jagoll last updated on 20/Mar/20 $$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{if}\: \\ $$$$\mathrm{f}\:'\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{x}^{\mathrm{2}} \right)\:=\:\mathrm{2x}+\mathrm{1} \\ $$ Commented by mathmax by abdo last updated on 20/Mar/20 $${its}\:{clear}\:{that}\:{f}\:{is}\:{polynomial}\:{let}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{0}}…

x-4-x-2-1-dx-

Question Number 19666 by Joel577 last updated on 14/Aug/17 $$\int\:{x}^{\mathrm{4}} \sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:{dx} \\ $$ Answered by ajfour last updated on 14/Aug/17 $$\:\mathrm{I}=\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{x}^{\mathrm{3}} \left(\mathrm{2x}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right)\mathrm{dx} \\…

Question-150728

Question Number 150728 by ali1245 last updated on 14/Aug/21 Answered by tabata last updated on 15/Aug/21 $$\mathrm{2}{I}=_{{z}={x}\:} {Re}\:\left(\int_{−\infty} ^{\:\infty} \:\frac{{z}^{\:{a}−\mathrm{1}} }{\left({z}^{\mathrm{2}} +{c}\right)\left({z}^{\mathrm{2}} +{b}\right)}{dz}\right) \\ $$$$…