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Category: Integration

Question-109884

Question Number 109884 by 4635 last updated on 26/Aug/20 Commented by mohammad17 last updated on 26/Aug/20 $$ \\ $$$${set}:\:{y}={ln}^{{n}} {x}\rightarrow{x}={e}^{\frac{{y}}{{n}}} \rightarrow{dx}={e}^{\frac{{y}}{{n}}} \:\:\frac{{dy}}{{n}}\: \\ $$$${x}=\mathrm{1}\rightarrow{y}=\mathrm{0}\:,\:{x}={e}\rightarrow{y}=\mathrm{1} \\…

f-4-1-4-and-f-8-1-2-4-8-f-x-2-f-x-4-dx-1-then-f-6-

Question Number 175395 by infinityaction last updated on 29/Aug/22 $$\:\:\:\:\:{f}\left(\mathrm{4}\right)\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\:{and}\:\:\:\:{f}\left(\mathrm{8}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\int_{\mathrm{4}} ^{\mathrm{8}} \:\frac{\:\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{\left[{f}\left({x}\right)\right]^{\mathrm{4}} }{dx}\:\:=\:\:\mathrm{1}\:\:\:\:{then}\:\:\:{f}\left(\mathrm{6}\right)=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

let-f-x-x-e-t-t-dt-1-calculate-f-x-2-find-a-equivalent-of-f-x-when-x-

Question Number 44318 by abdo.msup.com last updated on 26/Sep/18 $${let}\:{f}\left({x}\right)=\int_{{x}} ^{+\infty} \:\frac{{e}^{−{t}} }{{t}}{dt} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{a}\:{equivalent}\:{of}\:{f}\left({x}\right)\:{when} \\ $$$${x}\rightarrow+\infty. \\ $$ Commented by tanmay.chaudhury50@gmail.com…

J-0-pi-2-sin-x-1-sin-x-cos-x-dx-

Question Number 175387 by cortano1 last updated on 29/Aug/22 $$\:{J}=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:{dx} \\ $$ Commented by infinityaction last updated on 29/Aug/22 $$\:\:\:\:{J}\:\:\:=\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{2sin}\frac{{x}}{\mathrm{2}}\mathrm{cos}\:\frac{{x}}{\mathrm{2}}\:}{\mathrm{2sin}\frac{{x}}{\mathrm{2}}\:\mathrm{cos}\frac{{x}}{\mathrm{2}}\:+\mathrm{2cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}\:}{dx}…