Question Number 146067 by gsk2684 last updated on 10/Jul/21 $${transform}\:{the}\:{cartesian}\:{inyegral}\: \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} {\int}}{e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} \:{dy}\:{dx}\:{into}\:{polar}\:{integral}\: \\ $$$${and}\:{evaluate}\:{it}. \\ $$ Answered…
Question Number 146062 by mnjuly1970 last updated on 10/Jul/21 $$ \\ $$$$\:\:\:\:{find}\:\:{values}\:\:{a}\:,\:{b}\:,\:{c}\:\:{such}\:{that}: \\ $$$$\:\:\:\:−\mathrm{1}\leqslant\:{ax}\:^{\mathrm{2}} +{bx}\:+{c}\:\leqslant\:\mathrm{1} \\ $$$$\:\:\:\:\:\:{and}\:\:\frac{\mathrm{6}{b}^{\:\mathrm{2}} +\:\mathrm{8}\:{a}^{\:\mathrm{2}} }{\mathrm{3}}\:{is}\:{Max}… \\ $$ Commented by mr W…
Question Number 146035 by KONE last updated on 10/Jul/21 $${help}\:{me}\:{please} \\ $$$$\int\frac{{ln}\left({x}+\mathrm{1}\right)}{{x}}{dx}=?? \\ $$$$ \\ $$ Answered by KONE last updated on 10/Jul/21 $${please} \\…
Question Number 80485 by jagoll last updated on 03/Feb/20 $${what}\:{is}\:{the}\:{king}\:\:{rule}? \\ $$ Commented by mr W last updated on 03/Feb/20 $${in}\:{mathematics}? \\ $$$${then}\:{king}\:{rule}\:{is} \\ $$$$\int_{{a}}…
Question Number 80452 by abdomathmax last updated on 03/Feb/20 $${find}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by abdomathmax last updated on 03/Mar/20 $${I}=\:{Re}\left(\int_{−\infty}…
Question Number 80451 by abdomathmax last updated on 03/Feb/20 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left(\pi{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by abdomathmax last updated on 04/Feb/20 $${let}\:{I}=\int_{\mathrm{0}} ^{\infty}…
Question Number 80432 by Power last updated on 03/Feb/20 Commented by mr W last updated on 03/Feb/20 Commented by john santu last updated on 03/Feb/20…
Question Number 80416 by jagoll last updated on 03/Feb/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{x}\mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$ Answered by MJS last updated on 03/Feb/20 $$\int\frac{{x}\mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }{dx}= \\…
Question Number 80397 by M±th+et£s last updated on 02/Feb/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\:\sqrt[{{y}}]{{x}^{\pi} }\:+\mathrm{1}}\:{dx}\:{dy}\:=\mathrm{2}{c}\: \\ $$$${whrre}\:{c}\:{denote}\:{tha}\:{catalan}^{,} {s}\:{constant} \\ $$ Commented by mathmax…
Question Number 80369 by M±th+et£s last updated on 02/Feb/20 Commented by mathmax by abdo last updated on 03/Feb/20 $${let}\:{A}\:=\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \:\:\:\left(\mathrm{1}+{u}^{\mathrm{2}} \:+{v}^{\mathrm{2}} \:+{w}^{\mathrm{2}} \right)^{−\mathrm{2}} {dudvdw}…