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Category: Integration

Question-199942

Question Number 199942 by cortano12 last updated on 11/Nov/23 Answered by MM42 last updated on 11/Nov/23 $$\mathrm{1}−\sqrt{{x}}={u}^{\mathrm{2}} \Rightarrow{x}=\left(\mathrm{1}−{u}^{\mathrm{2}} \right)^{\mathrm{2}} ={x}\Rightarrow{dx}=−\mathrm{4}{u}\left(\mathrm{1}−{u}^{\mathrm{2}} \right){du} \\ $$$$\left.\Rightarrow{I}=\mathrm{4}\int_{\mathrm{0}} ^{\mathrm{1}} \left({u}^{\mathrm{2}}…

I-0-pi-2-tan-1-sinx-2-dx-

Question Number 199570 by universe last updated on 05/Nov/23 $$\:\:\:\:\:\:\:\:\mathrm{I}\:\:\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{sin}{x}\:}{\mathrm{2}}\right){dx} \\ $$ Answered by witcher3 last updated on 05/Nov/23 $$\mathrm{I}\left(\mathrm{a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{tan}^{−\mathrm{1}}…

Question-199468

Question Number 199468 by Calculusboy last updated on 04/Nov/23 Answered by witcher3 last updated on 04/Nov/23 $$\frac{\mathrm{x}}{\mathrm{2021}\pi}\Leftrightarrow \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{e}^{\mathrm{t}^{\mathrm{2021}} } }\left(\mathrm{1}+\mathrm{t}^{\mathrm{2022}} \right)^{\frac{\mathrm{1}}{\mathrm{2022}}} \mathrm{dt}=\mathrm{I}…

R-cos-max-x-3-y-3-2-dx-dy-where-R-0-1-0-1-

Question Number 199377 by universe last updated on 02/Nov/23 $$\:\:\int\underset{\mathrm{R}} {\int}\mathrm{cos}\:\left(\mathrm{max}\left\{\mathrm{x}^{\mathrm{3}} ,\:\mathrm{y}^{\mathrm{3}/\mathrm{2}} \right\}\right)\mathrm{dx}\:\mathrm{dy}\:,\:\mathrm{where}\:\mathrm{R}\:=\:\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$ Answered by witcher3 last updated on 04/Nov/23 $$\mathrm{i}\:\mathrm{will}\:\mathrm{Try} \\ $$…

1-1-1-x-2-1-x-2-1-1-x-2-y-2-1-1-y-2-x-2-y-2-z-2-5-2-dx-dy-dz-is-

Question Number 199369 by universe last updated on 02/Nov/23 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \:\int_{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}} ^{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }} ^{\mathrm{1}+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} {dx}\:{dy}\:{dz}\:\:{is}…

Question-199213

Question Number 199213 by emilagazade last updated on 29/Oct/23 Answered by witcher3 last updated on 29/Oct/23 $$\int_{\mathrm{a}} ^{\mathrm{b}} \left(\mathrm{x}−\left[\mathrm{x}\right]−\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{dx} \\ $$$$=\underset{\mathrm{k}=\mathrm{a}} {\overset{\mathrm{b}−\mathrm{1}} {\sum}}\int_{\mathrm{k}} ^{\mathrm{k}+\mathrm{1}} \left(\mathrm{x}−\left[\mathrm{x}\right]−\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{f}'\left(\mathrm{x}\right)\mathrm{dx}…