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Category: Integration

if-2x-3-2-a-x-f-t-dt-then-f-a-

Question Number 134884 by abdullahquwatan last updated on 08/Mar/21 $$\mathrm{if}\:\mathrm{2x}^{\mathrm{3}} −\mathrm{2}=\int_{{a}} ^{\mathrm{x}} \mathrm{f}\left(\mathrm{t}\right)\mathrm{dt},\:\mathrm{then}\:\mathrm{f}\:'\left({a}\right)=… \\ $$ Answered by bemath last updated on 08/Mar/21 $$\:\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:\mathrm{2x}^{\mathrm{3}} −\mathrm{2}\:\right]=\:\mathrm{f}\left(\mathrm{x}\right) \\…

let-U-n-0-cos-nx-x-2-n-2-2-dx-calculate-lim-n-e-n-2-U-n-

Question Number 134866 by mathmax by abdo last updated on 07/Mar/21 $$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}\left(\mathrm{nx}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{n}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dx}\:\mathrm{calculate}\:\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{e}^{\mathrm{n}^{\mathrm{2}} } \mathrm{U}_{\mathrm{n}} \\ $$ Answered by…

Question-134820

Question Number 134820 by 0731619177 last updated on 07/Mar/21 Answered by Ar Brandon last updated on 07/Mar/21 $$\mathcal{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{xyz}}{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{z}\right)\left(\mathrm{z}+\mathrm{y}\right)}\mathrm{dxdydz} \\…

0-pi-2-sin-3x-2-tan-3x-dx-

Question Number 134811 by bramlexs22 last updated on 07/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{sin}\:\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)}{\mathrm{tan}\:\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on 07/Mar/21 $$\mathrm{set}\:\frac{\mathrm{3x}}{\mathrm{2}}\:=\:\mathrm{t}\:\Rightarrow\:\mathrm{3x}\:=\:\mathrm{2t}\:,\:\begin{array}{|c|c|}{\mathrm{x}=\frac{\pi}{\mathrm{2}}\rightarrow\mathrm{t}=\frac{\mathrm{3}\pi}{\mathrm{4}}}\\{\mathrm{x}=\mathrm{0}\:\rightarrow\mathrm{t}=\mathrm{0}}\\\hline\end{array} \\ $$$$\mathbb{L}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{3}\pi/\mathrm{4}}…

Question-134795

Question Number 134795 by 0731619177 last updated on 07/Mar/21 Answered by EDWIN88 last updated on 07/Mar/21 $$\:\mathrm{noting}\:\mathrm{that}\:\mathrm{the}\:\mathrm{integrand}\:\mathrm{is}\:\mathrm{even}\:\mathrm{function} \\ $$$$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:\left(\pi\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{\infty} \frac{\mathrm{sin}\:\left(\pi\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}…