Menu Close

Category: Integration

Prove-that-for-all-a-gt-0-a-a-arg-1-2-ix-dx-0-Deduce-that-f-x-arg-1-2-ix-is-an-old-function-on-R-

Question Number 120554 by snipers237 last updated on 01/Nov/20 $${Prove}\:{that}\:{for}\:{all}\:\:{a}>\mathrm{0} \\ $$$$\int_{\left[−{a};{a}\right]} {arg}\left(\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\:−{ix}\right)\right){dx}\:=\mathrm{0} \\ $$$${Deduce}\:{that}\: \\ $$$${f}:\:{x}\rightarrow{arg}\left(\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\:−{ix}\right)\right)\:\:{is}\:{an}\:{old}\:{function}\:{on}\:\mathbb{R} \\ $$ Terms of Service Privacy Policy Contact:…

Question-120549

Question Number 120549 by bobhans last updated on 01/Nov/20 Answered by TANMAY PANACEA last updated on 01/Nov/20 $$\frac{−\mathrm{1}}{\mathrm{4}}\int\frac{−\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{3}−\mathrm{4}{x}−\mathrm{3}}{\left(\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx} \\ $$$$=\frac{−\mathrm{1}}{\mathrm{4}}\int\frac{{dx}}{\:\sqrt{\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} }}+\frac{\mathrm{1}}{\mathrm{4}}\int\frac{\mathrm{4}{x}+\mathrm{3}}{\left(\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}}…

x-3-x-2-1-3-dx-

Question Number 54995 by peter frank last updated on 15/Feb/19 $$\int\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by MJS last updated on 16/Feb/19 $$\mathrm{I}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{of}\:\mathrm{typing}\:\mathrm{work} \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{need}\:\mathrm{it}\:\mathrm{urgently}\:\mathrm{I}\:\mathrm{will}\:\mathrm{post}\:\mathrm{it}…

let-f-0-1-x-2-2-cos-x-1-dx-with-R-1-calculate-f-2-find-the-value-of-g-0-1-xsin-x-2-2cos-x-1-dx-

Question Number 54936 by maxmathsup by imad last updated on 14/Feb/19 $${let}\:{f}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}}{dx}\:\:\:{with}\:\theta\:\in\:{R}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{g}\left(\theta\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xsin}\theta}{\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{cos}\theta\:{x}\:+\mathrm{1}}}{dx} \\ $$ Commented…