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Category: Integration

0-3-1-cos-x-2-dx-

Question Number 122542 by bramlexs22 last updated on 18/Nov/20 $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\sqrt{\mathrm{1}+\mathrm{cos}\:\left({x}^{\mathrm{2}} \right)}\:{dx}\:? \\ $$ Answered by Olaf last updated on 18/Nov/20 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{3}} \sqrt{\mathrm{1}+\mathrm{cos}\left({x}^{\mathrm{2}}…

nice-calculus-0-pi-2-xsin-x-cos-x-ln-sin-x-ln-cos-x-dx-pi-16-pi-3-192-

Question Number 122528 by mnjuly1970 last updated on 17/Nov/20 $$\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {xsin}\left({x}\right).{cos}\left({x}\right){ln}\left({sin}\left({x}\right).{ln}\left({cos}\left({x}\right)\right){dx}\right. \\ $$$$\overset{???} {=}\:\frac{\pi}{\mathrm{16}}−\frac{\pi^{\mathrm{3}} }{\mathrm{192}}\:\checkmark \\ $$ Answered by mindispower last updated…

Question-122506

Question Number 122506 by mathace last updated on 17/Nov/20 Answered by TANMAY PANACEA last updated on 17/Nov/20 $$\int\frac{{ln}\left(\mathrm{1}+\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} \right)}{{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx} \\ $$$${x}={seca} \\ $$$$\int\frac{{ln}\left(\mathrm{1}+{tan}^{\mathrm{4}}…

2-x-e-x-dx-

Question Number 188036 by Michaelfaraday last updated on 25/Feb/23 $$\int\mathrm{2}^{{x}} {e}^{{x}} {dx} \\ $$ Answered by MJS_new last updated on 25/Feb/23 $$\int\mathrm{2}^{{x}} \mathrm{e}^{{x}} {dx}=\int\mathrm{e}^{\left(\mathrm{1}+\mathrm{ln}\:\mathrm{2}\right){x}} {dx}=\frac{\mathrm{e}^{\left(\mathrm{1}+\mathrm{ln}\:\mathrm{2}\right){x}}…

V-0-3-x-dx-x-1-5x-1-T-pi-2-pi-2-cos-x-cos-3-x-dx-

Question Number 122496 by benjo_mathlover last updated on 17/Nov/20 $$\:\:{V}=\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{{x}\:{dx}}{\:\sqrt{{x}+\mathrm{1}}+\sqrt{\mathrm{5}{x}+\mathrm{1}}} \\ $$$$\:{T}=\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\sqrt{\mathrm{cos}\:{x}−\mathrm{cos}\:^{\mathrm{3}} {x}}\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated…

let-A-n-W-n-e-xy-x-2-y-2-dxdy-with-W-n-1-n-n-1-n-n-1-find-A-n-interms-of-n-2-determine-lim-n-A-n-

Question Number 56938 by maxmathsup by imad last updated on 26/Mar/19 $${let}\:{A}_{{n}} =\int\int_{{W}_{{n}} } {e}^{−{xy}} \sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}\:\:\:{with}\:{W}_{{n}} =\left[\frac{\mathrm{1}}{{n}},{n}\left[×\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.\right.\right. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}}…