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Category: Integration

1-0-10pi-sec-1-x-cot-1-x-dx-2-area-bounded-by-curve-y-ln-x-and-the-lines-y-0-y-ln-3-and-x-0-is-equal-to-

Question Number 59474 by rahul 19 last updated on 10/May/19 $$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\mathrm{10}\pi} \left(\left[\mathrm{sec}^{−\mathrm{1}} {x}\right]+\left[\mathrm{co}{t}^{−\mathrm{1}} {x}\right]\:\right)\:{dx}\:=\:? \\ $$$$\left.\mathrm{2}\right){area}\:{bounded}\:{by}\:{curve}\:{y}={ln}\left({x}\right)\:{and} \\ $$$${the}\:{lines}\:{y}=\mathrm{0},{y}={ln}\left(\mathrm{3}\right)\:{and}\:{x}=\mathrm{0}\:{is} \\ $$$${equal}\:{to}\:? \\ $$ Commented by…

Question-190533

Question Number 190533 by TUN last updated on 05/Apr/23 Answered by witcher3 last updated on 05/Apr/23 $$\frac{\mathrm{arctan}\left(\mathrm{x}\right)}{\mathrm{x}}=\underset{\mathrm{0}} {\int}^{\mathrm{1}} \frac{\mathrm{da}}{\mathrm{1}+\mathrm{a}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} } \\ $$$$\Leftrightarrow\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{tan}^{−\mathrm{1}}…

find-dx-x-1-2-x-1-2-

Question Number 124980 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{find}\:\int\:\:\frac{\mathrm{dx}}{\left(\sqrt{\mathrm{x}−\mathrm{1}}+\mathrm{2}\sqrt{\mathrm{x}+\mathrm{1}}\right)^{\mathrm{2}} } \\ $$ Answered by liberty last updated on 07/Dec/20 $$\: \\ $$$$\left[\:\:\frac{\sqrt{{x}+\mathrm{1}}−\mathrm{2}\sqrt{{x}+\mathrm{1}}}{{x}−\mathrm{1}−\mathrm{4}\left({x}+\mathrm{1}\right)}\:\right]^{\mathrm{2}}…

let-f-x-arctan-x-n-with-n-natural-1-find-f-n-0-and-f-n-1-2-developp-f-at-integr-serie-3-calculte-0-f-x-x-n-dx-with-n-2-

Question Number 124979 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{arctan}\left(\mathrm{x}^{\mathrm{n}} \right)\:\mathrm{with}\:\mathrm{n}\:\mathrm{natural} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\mathrm{calculte}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{n}} }\mathrm{dx}\:\mathrm{with}\:\mathrm{n}\geqslant\mathrm{2} \\…