Menu Close

Category: Integration

calculate-lim-n-a-n-0-1-x-2n-sin-pix-2-dx-with-a-n-k-1-n-sin-pik-2n-

Question Number 111771 by mathmax by abdo last updated on 04/Sep/20 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{a}_{\mathrm{n}} \int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{x}^{\mathrm{2n}} \mathrm{sin}\left(\frac{\pi\mathrm{x}}{\mathrm{2}}\right)\mathrm{dx}\:\mathrm{with}\:\mathrm{a}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\mathrm{sin}\left(\frac{\pi\mathrm{k}}{\mathrm{2n}}\right) \\ $$ Terms of Service…

f-function-continue-on-0-1-find-lim-n-1-n-k-0-n-n-k-k-n-k-1-n-f-x-dx-

Question Number 111770 by mathmax by abdo last updated on 04/Sep/20 $$\mathrm{f}\:\mathrm{function}\:\mathrm{continue}\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\frac{\mathrm{1}}{\mathrm{n}}\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \left(\mathrm{n}−\mathrm{k}\right)\int_{\frac{\mathrm{k}}{\mathrm{n}}} ^{\frac{\mathrm{k}+\mathrm{1}}{\mathrm{n}}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact:…

explicite-f-x-0-2pi-ln-x-2-2xcos-1-d-x-1-

Question Number 111768 by mathmax by abdo last updated on 04/Sep/20 $$\mathrm{explicite}\:\mathrm{f}\left(\mathrm{x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)\mathrm{d}\theta\:\:\:\:\:\:\:\:\left(\mathrm{x}\neq\overset{−} {+}\mathrm{1}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Prove-that-0-pi-2-sin-2-x-sin-x-cos-x-dx-1-2-log-2-1-

Question Number 177298 by peter frank last updated on 03/Oct/22 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}{\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)}\mathrm{dx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{log}\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right) \\ $$ Answered by Ar Brandon last updated on…

Question-46225

Question Number 46225 by rahul 19 last updated on 22/Oct/18 Answered by MrW3 last updated on 23/Oct/18 $${let}\:{f}\left({x}\right)={a}\left({x}−{b}\right)^{\mathrm{2}} +{c} \\ $$$$\left({b}\right)\Rightarrow{b}=\mathrm{1},\:{c}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left({a}\right)\Rightarrow{a}\left(\mathrm{0}−\mathrm{1}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0}\Rightarrow{a}=−\frac{\mathrm{1}}{\mathrm{2}} \\…