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Category: Integration

Question-114541

Question Number 114541 by mnjuly1970 last updated on 19/Sep/20 Answered by abdomsup last updated on 19/Sep/20 $${A}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{\mathrm{2}} {ln}\left({x}\right)}{\mathrm{1}−{x}^{\mathrm{2}} }{dx}\:\Rightarrow \\ $$$${A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}}…

calculus-evaluate-I-0-pi-2-tan-2x-sin-4-x-4cos-2-x-cos-4-x-4sin-2-x-dx-m-n-july-1970-

Question Number 114472 by mnjuly1970 last updated on 19/Sep/20 $$\:\:\:\:\:\:\:\:\:…\:\:{calculus}… \\ $$$${evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{tan}\left(\mathrm{2}{x}\right)}{\:\sqrt{{sin}^{\mathrm{4}} \left({x}\right)+\mathrm{4}{cos}^{\mathrm{2}} \left({x}\right)}−\sqrt{{cos}^{\mathrm{4}} \left({x}\right)+\mathrm{4}{sin}^{\mathrm{2}} \left({x}\right)\:}}\:{dx}=\:??? \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}…. \\…

Question-179991

Question Number 179991 by mnjuly1970 last updated on 05/Nov/22 Answered by mindispower last updated on 05/Nov/22 $$=\underset{{n}\geqslant\mathrm{2}} {\sum}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{{m}!}{x}^{{m}} {e}^{−{nx}} {dx}=\frac{\mathrm{1}}{{m}!}\int_{\mathrm{0}} ^{\infty} \left(\frac{{y}}{{n}}\right)^{{m}} {e}^{−{y}}…