Category: Integration

Question Number 65398 by mathmax by abdo last updated on 29/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} =\int\int_{\left[\mathrm{1},{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:\:{sin}\left({x}^{\mathrm{2}} \:+\mathrm{3}{y}^{\mathrm{2}} \right)\:{e}^{−{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} } {dxdy} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$…

Question Number 65395 by imron876 last updated on 29/Jul/19 Commented by mathmax by abdo last updated on 29/Jul/19 $$\int\:\left(−\mathrm{1}\right)^{{x}} {dx}\:=\int\:{e}^{{i}\pi{x}} {dx}\:=\frac{\mathrm{1}}{{i}\pi}{e}^{{i}\pi{x}} \:+{c}\:=\frac{\left(−\mathrm{1}\right)^{{x}} }{{i}\pi}\:+{c} \\ $$…

Question Number 130907 by greg_ed last updated on 30/Jan/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)}{{x}}\:{dx} \\ $$ Commented by benjo_mathlover last updated on 30/Jan/21 այս հարցն արդեն պատասխանվել է Commented by…

Question Number 65355 by mathmax by abdo last updated on 28/Jul/19 $${find}\:\int\:\:\:\frac{{dx}}{\:\sqrt{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)}} \\ $$ Commented by Prithwish sen last updated on 29/Jul/19 $$\int\frac{\mathrm{dx}}{\:\sqrt{\left\{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{1}\right\}\left(\mathrm{x}+\mathrm{2}\right)}}\:\:\:\mathrm{putting}\:\left(\mathrm{x}+\mathrm{2}\right)=\mathrm{a} \\…

Question Number 65352 by mathmax by abdo last updated on 28/Jul/19 $${give}\:{the}\:{integralA}_{{n}} =\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dt}}{\mathrm{1}+{x}^{{n}} }\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$${at}\:{form}\:{of}\:{serie}. \\ $$ Commented by mathmax by abdo…