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Category: Integration

Nice-calculus-evaluate-S-n-1-2-2n-1-cos-pi-2-n-M-N-1970-

Question Number 120875 by mnjuly1970 last updated on 03/Nov/20 $$\:\:\:\:\:\:\:\:\:\:…\:\mathscr{N}{ice}\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:{S}=\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{2}^{−\mathrm{2}{n}} }{\mathrm{1}+{cos}\left(\frac{\pi}{\mathrm{2}^{{n}} }\right)}\right)=??\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\mathscr{M}.\mathscr{N}.\mathrm{1970}… \\ $$ Terms…

3x-3x-3-7-dx-

Question Number 55310 by afachri last updated on 21/Feb/19 $$ \\ $$$$\int\:\mathrm{3}{x}\sqrt{\:\mathrm{3}{x}^{\mathrm{3}} +\:\mathrm{7}}\:\:{dx}\:=\:\:.\:.\:.\:. \\ $$ Commented by MJS last updated on 22/Feb/19 $$\mathrm{where}\:\mathrm{does}\:\mathrm{this}\:\mathrm{come}\:\mathrm{from}? \\ $$$$\mathrm{I}\:\mathrm{tried}\:\mathrm{everything}\:\mathrm{I}\:\mathrm{know}\:\mathrm{but}\:\mathrm{it}\:\mathrm{seems}…

1-2-tan-1-x-2-x-2-dx-

Question Number 186352 by normans last updated on 03/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{1}} ^{\:\mathrm{2}} \:\:\frac{\boldsymbol{{tan}}^{−\mathrm{1}} \:\left(\boldsymbol{{x}}\right)\:+\:\mathrm{2}}{\boldsymbol{{x}}^{\mathrm{2}} }\:\:\boldsymbol{{dx}}\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered by MJS_new last updated…

calculatef-a-1-a-x-2-arctan-a-x-dx-2-calculate-1-1-2-x-2-arctan-2-x-dx-

Question Number 55282 by Abdo msup. last updated on 20/Feb/19 $${calculatef}\left({a}\right)=\:\:\int\:\:\:\left(\mathrm{1}+\frac{{a}}{{x}^{\mathrm{2}} }\right){arctan}\left(\frac{{a}}{{x}}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{1}} ^{+\infty} \left(\mathrm{1}+\frac{\mathrm{2}}{{x}^{\mathrm{2}} }\right){arctan}\left(\frac{\mathrm{2}}{{x}}\right){dx}\:. \\ $$ Commented by maxmathsup by imad last…

let-a-1-3-arctan-a-x-dx-1-calculate-a-interms-of-a-2-calculate-a-at-form-of-integral-3-determine-n-a-at-form-of-integral-4-find-the-value-of-1-3-arctan-2

Question Number 55274 by maxmathsup by imad last updated on 20/Feb/19 $${let}\:\varphi\left({a}\right)\:=\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \:\:{arctan}\left(\frac{{a}}{{x}}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\varphi\left({a}\right)\:{interms}\:{of}\:{a} \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:\varphi^{'} \left({a}\right)\:{at}\:{form}\:{of}\:{integral}. \\ $$$$\left.\mathrm{3}\right)\:{determine}\:\varphi^{\left({n}\right)} \left({a}\right)\:\:{at}\:{form}\:{of}\:{integral}. \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}}…

let-f-x-x-2-1-x-dt-1-t-t-2-1-calculate-f-x-interms-of-x-2-calculate-lim-x-0-f-x-and-lim-x-f-x-

Question Number 55273 by maxmathsup by imad last updated on 20/Feb/19 $${let}\:\:{f}\left({x}\right)\:=\int_{{x}^{\mathrm{2}} } ^{\mathrm{1}+{x}} \:\:\frac{{dt}}{\mathrm{1}+{t}+{t}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right)\:{interms}\:{of}\:{x} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} \:\:{f}\left({x}\right) \\ $$ Commented…