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Category: Integration

Triangle-AOC-inscribed-in-the-region-cut-from-the-parabola-y-x-2-by-the-line-y-a-2-Find-the-limit-of-ratio-of-the-area-of-the-triangle-to-the-area-of-the-parabolic-region-as-a-approaches-zero-

Question Number 144638 by liberty last updated on 27/Jun/21 $$\mathrm{Triangle}\:\mathrm{AOC}\:\mathrm{inscribed} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{region}\:\mathrm{cut}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} \:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{line}\:\mathrm{y}=\mathrm{a}^{\mathrm{2}} \:.\mathrm{Find}\:\mathrm{the}\:\mathrm{limit} \\ $$$$\mathrm{of}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{triangle}\:\mathrm{to}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{parabolic}\:\mathrm{region}\:\mathrm{as}\:\mathrm{a}\:\mathrm{approaches} \\…

if-cos-f-x-dx-g-x-sin-f-x-dx-use-g-x-

Question Number 79086 by key of knowledge last updated on 22/Jan/20 $$\mathrm{if}:\int\mathrm{cos}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}=\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\int\mathrm{sin}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}=?\:\left(\mathrm{use}\:\mathrm{g}\left(\mathrm{x}\right)\right) \\ $$ Commented by mr W last updated on 23/Jan/20 $${how}\:{did}\:{you}\:{get}…

let-x-1-3-cosx-developp-f-at-fourier-serie-

Question Number 144597 by mathmax by abdo last updated on 26/Jun/21 $$\mathrm{let}\:\varphi\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{3}+\mathrm{cosx}} \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by Olaf_Thorendsen last updated on 26/Jun/21 $${a}_{\mathrm{0}} \:=\:\frac{\mathrm{1}}{\mathrm{T}}\int_{−\frac{\mathrm{T}}{\mathrm{2}}}…