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Category: Integration

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}}}…

Find-the-volume-of-the-region-bounded-by-the-elliptic-paraboloid-z-4-x-2-1-4-y-2-and-the-plane-z-0-

Question Number 144528 by imjagoll last updated on 26/Jun/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\: \\ $$$$\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{elliptic}\:\mathrm{paraboloid} \\ $$$$\mathrm{z}\:=\:\mathrm{4}−\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\mathrm{y}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{z}=\mathrm{0} \\ $$$$ \\ $$ Answered by EDWIN88 last updated…

Calculus-I-P-0-pi-2-xcos-x-1-e-sin-x-dx-0-pi-2-xsin-x-1-e-cos-x-dx-

Question Number 144527 by mnjuly1970 last updated on 26/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:…..\:\:\:\mathrm{Calculus}\:\:\left(\mathrm{I}\:\right)….. \\ $$$$\mathrm{P}:=\:\frac{\int_{\mathrm{0}\:} ^{\:\:\frac{\pi}{\mathrm{2}}} \left(\:{xcos}\left({x}\right)+\mathrm{1}\:\right){e}^{\:{sin}\left({x}\right)} {dx}\:}{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\:{xsin}\left({x}\right)\:−\mathrm{1}\:\right){e}^{\:{cos}\left({x}\:\right)} {dx}}=? \\ $$ Answered by Kamel…

Calculus-I-Lim-x-0-1-cos-xcos-x-2-cos-x-4-cos-x-8-x-2-

Question Number 144450 by mnjuly1970 last updated on 25/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:………\mathrm{C}{alculus}\left(\mathrm{I}\right)……… \\ $$$$\:\:\mathrm{Lim}_{\:\:{x}\:\rightarrow\:\mathrm{0}} \frac{\mathrm{1}\:−{cos}\left({xcos}\left(\frac{{x}}{\mathrm{2}}\right).{cos}\left(\frac{{x}}{\mathrm{4}}\right){cos}\left(\frac{{x}}{\mathrm{8}}\right)\right)}{{x}^{\:\mathrm{2}} }=? \\ $$ Answered by Dwaipayan Shikari last updated on…