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Category: Integration

dx-sin3x-sin4x-

Question Number 62185 by aliesam last updated on 17/Jun/19 $$\int\frac{{dx}}{{sin}\mathrm{3}{x}+{sin}\mathrm{4}{x}} \\ $$ Answered by MJS last updated on 17/Jun/19 $$\int\frac{{dx}}{\mathrm{sin}\:\mathrm{3}{x}\:+\mathrm{sin}\:\mathrm{4}{x}}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\mathrm{1}}{\mathrm{cos}\:{x}}\:\rightarrow\:{dx}=\frac{\mathrm{cos}^{\mathrm{2}} \:{x}}{\mathrm{sin}\:{x}}\right] \\ $$$$=−\int\frac{{t}^{\mathrm{3}}…

if-f-x-x-n-2n-x-2n-1-n-1-2n-1-x-2n-2-where-n-0-1-2-3-9-find-0-20-f-x-dx-

Question Number 127704 by NATTAPONG4359 last updated on 01/Jan/21 $$ \\ $$$${if}\:{f}\left({x}\right)=\begin{cases}{{x}−{n}\:;\:\mathrm{2}{n}\:\leqslant\:{x}\:\leqslant\mathrm{2}{n}+\mathrm{1}}\\{{n}+\mathrm{1}\:;\:\mathrm{2}{n}+\mathrm{1}\leqslant{x}\leqslant\mathrm{2}{n}+\mathrm{2}\:}\end{cases}\:{where}\:\:{n}\:=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},..,\mathrm{9} \\ $$$${find}\:\int_{\mathrm{0}} ^{\mathrm{20}} {f}\left({x}\right){dx} \\ $$ Answered by mahdipoor last updated on 01/Jan/21…

let-A-0-dx-x-2-i-2-i-2-1-1-calculate-A-2-let-R-Re-A-and-I-Im-A-find-the-value-of-R-and-I-

Question Number 62141 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{i}\right)^{\mathrm{2}} }\:\:\:\:\:\left(\:{i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{R}\:={Re}\left({A}\right)\:{and}\:{I}\:={Im}\left({A}\right) \\ $$$${find}\:\:{the}\:{value}\:{of}\:{R}\:{and}\:{I}\:. \\ $$…

let-U-n-0-cos-nx-x-2-n-2-3-dx-with-n-1-1-calculate-U-n-intrems-of-n-2-find-lim-n-n-U-n-3-calculate-lim-n-n-2-U-n-4-study-the-convervence-of-U-n-

Question Number 62128 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx}\:\:{with}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{intrems}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {n}\:{U}_{{n}} \\…