Question Number 59162 by maxmathsup by imad last updated on 05/May/19 $${calculate}\:\:\int\int_{{D}} \:\:\sqrt{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{xy}\:{dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:\:\:/\mathrm{0}\leqslant{y}\leqslant\mathrm{1}\:\:{and}\:\:\mathrm{2}\:\leqslant{x}\:\leqslant\mathrm{5}\:\right\} \\ $$ Terms of Service Privacy Policy…
Question Number 59161 by maxmathsup by imad last updated on 05/May/19 $${calculatef}\left({a}\right)=\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dx}\:\:\:{with}\:>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)}{\mathrm{2}+{x}^{\mathrm{2}} }{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty}…
Question Number 59160 by maxmathsup by imad last updated on 05/May/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({xcos}\theta\right)}{{x}^{\mathrm{2}} \:+\theta^{\mathrm{2}} }\:{d}\theta\:\:\:\:\:\:{and}\:\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{sin}\left({xcos}\theta\right)}{{x}^{\mathrm{2}} \:+\theta^{\mathrm{2}} }\:{d}\theta \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty}…
Question Number 124672 by sdfg last updated on 05/Dec/20 $$\int_{−\mathrm{3}} ^{−\mathrm{2}} \left({y}+\mathrm{3}\right)^{\mathrm{6}} \left({y}+\mathrm{2}\right)^{\mathrm{4}} {dy} \\ $$ Commented by mohammad17 last updated on 05/Dec/20 $${put}:{n}={y}+\mathrm{3}\Rightarrow{y}={n}−\mathrm{3}\Rightarrow{dy}={dn} \\…
Question Number 124675 by sdfg last updated on 05/Dec/20 $$\int_{\mathrm{1}} ^{\mathrm{3}} \left({x}−\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{3}−{x}\right)^{\mathrm{2}} {dx} \\ $$ Commented by mohammad17 last updated on 05/Dec/20 $${put}:{m}={x}−\mathrm{1}\Rightarrow{x}={m}+\mathrm{1}\Rightarrow{dx}={dm} \\…
Question Number 124654 by benjo_mathlover last updated on 05/Dec/20 $$\:\underset{\mathrm{1}/\sqrt{\mathrm{2}}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\:\frac{{e}^{\mathrm{cos}^{−\mathrm{1}} \left({x}\right)} }{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx}\:?\: \\ $$ Commented by mohammad17 last updated on 05/Dec/20 $$…
Question Number 124644 by benjo_mathlover last updated on 05/Dec/20 $$\underset{\mathrm{2}/\sqrt{\mathrm{3}}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{cos}\:\left(\mathrm{sec}^{−\mathrm{1}} {x}\right)}{{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:{dx}\: \\ $$$$\underset{\:\sqrt{\mathrm{2}}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{sec}\:^{\mathrm{2}} \left(\mathrm{sec}^{−\mathrm{1}} {x}\right)}{{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:{dx}\: \\ $$ Answered by…
Question Number 190172 by jlewis last updated on 29/Mar/23 $${Integrate}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{Sin}^{\mathrm{2}} \left(\mathrm{2}\Pi{x}\right){dx} \\ $$ Answered by mehdee42 last updated on 29/Mar/23 $$\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}}…
Question Number 190168 by TUN last updated on 29/Mar/23 $$\left.\mathrm{1}\right)\underset{\mathrm{0}} {\int}^{\infty} \frac{{sin}\:{x}}{{x}^{{p}} +{sin}\:{x}}{dx}\:,{p}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\underset{\pi} {\int}^{\infty} \frac{{xcos}\:{x}}{{x}^{{p}} +{x}^{{q}} }{dx},{p}>\mathrm{0}{and}\:{q}>\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\underset{\mathrm{0}} {\int}^{\infty} \frac{{sin}\:{x}^{{p}} }{\:{x}^{{q}} }{dx},\:{p}>\mathrm{0},{q}>\mathrm{0}…
Question Number 124632 by liberty last updated on 05/Dec/20 $${Calculate}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:\sqrt{\frac{\mathrm{2}+{x}}{\mathrm{2}−{x}}}\:{dx}\: \\ $$ Answered by bemath last updated on 05/Dec/20 $${put}\:{x}=\mathrm{2cos}\:\mathrm{2}\theta\: \\ $$$${I}=\underset{\pi/\mathrm{4}} {\overset{\mathrm{0}}…