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Category: Integration

please-help-me-to-find-this-a-D-ydxdy-a-2-x-2-D-x-0-y-0-x-2-y-2-a-2-b-v-x-y-z-2-dxdydz-v-x-0-y-0-z-0-x-z-1-y-z-1-c-V-xydxdydz-V-0-z-1-x-2-y-2-

Question Number 170545 by kndramaths last updated on 26/May/22 $$\:\:\:\:{please}\:{help}\:{me}\:{to}\:{find}\:{this}. \\ $$$$\:\:\:{a}=\:\int\int_{{D}} \frac{{ydxdy}}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }\:{D}:\left\{{x}\geqslant\mathrm{0}.{y}\geqslant\mathrm{0}.{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant{a}^{\mathrm{2}} \right\} \\ $$$$\:\:\:{b}=\int\int\int_{{v}} \left({x}−{y}+{z}\right)^{\mathrm{2}} {dxdydz} \\ $$$$\:\:{v}:\left\{{x}=\mathrm{0}.{y}=\mathrm{0}.{z}=\mathrm{0}\:{x}+{z}=\mathrm{1}.{y}+{z}=\mathrm{1}\right\} \\…

c-cosxsiny-xy-dx-sinx-cosy-dy-faind-integral-on-the-opposite-sid-of-the-clock-face-in-the-c-unit-circle-solve-this-

Question Number 170535 by mathlove last updated on 26/May/22 $$\int_{{c}} \left({cosxsiny}−{xy}\right){dx}+\left({sinx}\:\centerdot{cosy}\right){dy} \\ $$$${faind}\:{integral}\:{on}\:{the}\:{opposite} \\ $$$${sid}\:{of}\:{the}\:{clock}\:{face}\:{in}\:{the} \\ $$$${c}\:{unit}\:{circle}? \\ $$$${solve}\:{this} \\ $$ Commented by mathlove last…

Let-I-n-x-n-e-x-dx-n-0-1-2-i-Show-that-I-n-x-n-e-x-nI-n-1-ii-Show-that-0-x-n-e-x-dx-n-

Question Number 170532 by MikeH last updated on 26/May/22 $$\mathrm{Let}\:{I}_{{n}} \:=\int{x}^{{n}} {e}^{−{x}} {dx},\:{n}\:=\:\mathrm{0},\mathrm{1},\mathrm{2},… \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Show}\:\mathrm{that}\:{I}_{{n}} \:=\:−{x}^{{n}} {e}^{−{x}} +{nI}_{{n}−\mathrm{1}} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} {x}^{{n}} {e}^{−{x}} {dx}\:=\:{n}! \\…

lim-n-1-n-2-1-2-n-2-2-3-n-2-3-1-n-1-

Question Number 39443 by rahul 19 last updated on 06/Jul/18 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left[\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}+\:\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2}}+\:\frac{\mathrm{3}}{\mathrm{n}^{\mathrm{2}} +\mathrm{3}}+\:….+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right]\:=\:? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 06/Jul/18 $${very}\:{good}…{this}\:{is}\:{the}\:{way}\:{to}\:{solve}\:{it}……

f-x-0-x-e-t-1-sin-t-1-cos-t-dt-Then-f-pi-3-f-2pi-3-

Question Number 39440 by rahul 19 last updated on 06/Jul/18 $$\mathrm{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\:{x}_{} } \:{e}^{{t}\:} \left(\frac{\mathrm{1}+\mathrm{sin}\:{t}}{\mathrm{1}+\mathrm{cos}\:{t}}\right)\:{dt}. \\ $$$${T}\mathrm{hen}\:\:\mathrm{f}\left(\frac{\pi}{\mathrm{3}}\right)×\mathrm{f}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\:=\:? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…