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Category: Integration

I-2-0-tan-1-x-x-2-dx-I-3-0-tan-1-x-x-3-dx-I-4-0-tan-1-x-x-4-dx-

Question Number 182291 by Frix last updated on 07/Dec/22 $${I}_{\mathrm{2}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}\right)^{\mathrm{2}} {dx}=?? \\ $$$${I}_{\mathrm{3}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}\right)^{\mathrm{3}} {dx}=??? \\ $$$${I}_{\mathrm{4}} =\underset{\mathrm{0}}…

the-curve-y-f-x-is-rotated-about-the-x-axis-to-form-solid-the-volume-of-this-solid-is-0-5pi-a-2sina-cosa-for-the-limit-of-0-x-a-find-the-value-of-a-

Question Number 116742 by Eric002 last updated on 06/Oct/20 $${the}\:{curve}\:{y}={f}\left({x}\right)\:{is}\:{rotated}\:{about}\:{the} \\ $$$${x}−{axis}\:{to}\:{form}\:{solid}.{the}\:{volume}\:{of}\:{this} \\ $$$${solid}\:{is}\:\mathrm{0}.\mathrm{5}\pi\left({a}−\mathrm{2}{sina}\:{cosa}\right)\:{for}\:{the}\:{limit} \\ $$$${of}\:\mathrm{0}\leqslant{x}\leqslant{a}.\:{find}\:{the}\:{value}\:{of}\:{a} \\ $$$$ \\ $$ Terms of Service Privacy Policy…

nice-calculus-prove-that-1-e-4x-x-1-dx-pi-2-e-4-m-n-1970-

Question Number 116744 by mnjuly1970 last updated on 06/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\frac{\:{nice}}{{calculus}}\:… \\ $$$$\:\:{prove}\:\:{that}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{−\mathrm{1}} ^{\:\infty} \frac{{e}^{−\mathrm{4}{x}} }{\:\sqrt{{x}+\mathrm{1}}}\:{dx}\:=\frac{\sqrt{\pi}}{\mathrm{2}}\:{e}^{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{m}.{n}\:.\mathrm{1970}… \\ $$$$ \\ $$…