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Category: Integration

x-2-1-x-2-dx-

Question Number 9467 by tawakalitu last updated on 09/Dec/16 $$\int\mathrm{x}^{\mathrm{2}} \left(\sqrt{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\right)\:\mathrm{dx} \\ $$ Answered by mrW last updated on 09/Dec/16 $$\mathrm{x}=\mathrm{sin}\:\mathrm{t} \\ $$$$\mathrm{dx}=\mathrm{cos}\:\mathrm{t}\:\mathrm{dt} \\…

Question-140490

Question Number 140490 by benjo_mathlover last updated on 08/May/21 Commented by john_santu last updated on 08/May/21 $$\frac{\pi}{\mathrm{2}}\:\left(\sqrt{\mathrm{2}\sqrt{\mathrm{2}}+\mathrm{2}}\:−\mathrm{2}\:\right)\:\approx\:\mathrm{0}.\mathrm{31} \\ $$ Answered by MJS_new last updated on…

Question-140447

Question Number 140447 by 676597498 last updated on 07/May/21 Answered by EDWIN88 last updated on 07/May/21 $$\mathrm{L}+\mathrm{M}=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{L}+\mathrm{M}\:=\:\underset{\mathrm{0}}…

find-x-3-x-1-2-x-dx-

Question Number 74890 by abdomathmax last updated on 03/Dec/19 $${find}\:\int\:\:\:\left({x}+\mathrm{3}\right)\sqrt{\left({x}−\mathrm{1}\right)\left(\mathrm{2}−{x}\right)}{dx} \\ $$ Commented by mathmax by abdo last updated on 04/Dec/19 $${let}\:{I}\:=\int\:\left({x}+\mathrm{3}\right)\sqrt{\left({x}−\mathrm{1}\right)\left(\mathrm{2}−{x}\right)}{dx}\:\:{changement}\:\sqrt{{x}−\mathrm{1}}={t}\:{give} \\ $$$${x}−\mathrm{1}={t}^{\mathrm{2}} \:\Rightarrow{I}\:=\int\left({t}^{\mathrm{2}}…