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Category: Integration

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

Question Number 104890 by Ar Brandon last updated on 24/Jul/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\mathrm{1}+\frac{\mathrm{k}^{\mathrm{3}} }{\mathrm{n}^{\mathrm{3}} }\right]^{−\frac{\mathrm{1}}{\mathrm{2}}} \\ $$ Answered by abdomathmax last updated on 24/Jul/20…

Let-f-x-0-2-x-t-dt-x-gt-0-then-minimum-value-of-f-x-is-

Question Number 39342 by rahul 19 last updated on 05/Jul/18 $$\mathrm{Let}\:\mathrm{f}\left({x}\right)\:=\:\int_{\mathrm{0}\:} ^{\mathrm{2}} \:\mid{x}−{t}\mid\:\mathrm{dt}\:\left({x}>\mathrm{0}\right)\:,\:\mathrm{then} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left({x}\right)\:\mathrm{is}\:? \\ $$ Answered by MrW3 last updated on 05/Jul/18 $${for}\:\mathrm{0}<{x}\leqslant\mathrm{2}:…

I-1-0-pi-sin-884x-sin-1122x-sin-x-dx-I-2-0-1-x-238-x-1768-1-x-2-1-dx-then-value-of-I-1-I-2-

Question Number 39341 by rahul 19 last updated on 05/Jul/18 $$\mathrm{I}_{\mathrm{1}} =\:\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{sin}\:\mathrm{884}{x}\:\mathrm{sin}\:\mathrm{1122}{x}}{\mathrm{sin}\:{x}}\:{dx} \\ $$$$\mathrm{I}_{\mathrm{2}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{\mathrm{238}} \left({x}^{\mathrm{1768}} −\mathrm{1}\right)}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)}\:{dx} \\ $$$${then}\:{value}\:{of}\:\frac{\mathrm{I}_{\mathrm{1}} }{\mathrm{I}_{\mathrm{2}}…

If-f-x-0-4-e-t-x-dt-0-x-4-maximum-value-of-f-x-is-

Question Number 39338 by rahul 19 last updated on 05/Jul/18 $$\mathrm{If}\:\mathrm{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{4}} \:\mathrm{e}^{\mid\mathrm{t}−{x}\mid} \:\mathrm{dt}\:\:\:\:\left(\mathrm{0}\leqslant{x}\leqslant\mathrm{4}\right), \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left({x}\right)\:\mathrm{is}\:=\:? \\ $$ Commented by math khazana by abdo last…

x-2-9-x-3-dx-

Question Number 104851 by bemath last updated on 24/Jul/20 $$\int\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}{{x}^{\mathrm{3}} }\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 24/Jul/20 $$\int\frac{{t}^{\mathrm{2}} {dt}}{{x}^{\mathrm{4}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}}…

Prove-that-0-pi-2-ln-a-sin-2-x-dx-piln-a-1-a-1-pi-2-ln-a-4-a-gt-0-Im-a-0-

Question Number 170384 by amin96 last updated on 22/May/22 $$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right)\right)\boldsymbol{\mathrm{dx}}=\pi\boldsymbol{\mathrm{ln}}\left(\sqrt{\frac{\boldsymbol{\mathrm{a}}−\mathrm{1}}{\boldsymbol{\mathrm{a}}}}+\mathrm{1}\right)+\frac{\pi}{\mathrm{2}}\boldsymbol{\mathrm{ln}}\left(\frac{\boldsymbol{\mathrm{a}}}{\mathrm{4}}\right) \\ $$$$\boldsymbol{\mathrm{a}}>\mathrm{0}\:\:\:\:\boldsymbol{\mathrm{I}{m}}\left\{\boldsymbol{{a}}\right\}\neq\mathrm{0}\:\: \\ $$ Terms of Service Privacy Policy Contact:…