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Category: Integration

0-sin-x-x-dx-

Question Number 171117 by meetbhavsar25 last updated on 08/Jun/22 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{sin}\:{x}}{{x}}{dx}\:=\:\left(?\right) \\ $$ Answered by aleks041103 last updated on 08/Jun/22 $${f}\left({z}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{zx}} \frac{{sinx}}{{x}}{dx}…

let-f-t-0-pi-2-ln-cosx-t-sinx-1-calculate-f-0-2-calculate-f-t-then-find-a-simple-form-of-f-t-3-calculate-0-pi-2-ln-cosx-2-sinx-dx-4-calculate-0-pi-2-ln-3-cosx-sinx-d

Question Number 40044 by abdo mathsup 649 cc last updated on 15/Jul/18 $${let}\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\:{cosx}\:+{t}\:{sinx}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({t}\right)\:{then}\:{find}\:\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cosx}\:+\mathrm{2}\:{sinx}\right){dx} \\…

Question-171108

Question Number 171108 by akolade last updated on 08/Jun/22 Answered by qaz last updated on 08/Jun/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{3}} −\mathrm{2x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{5}} }{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{7}} }\mathrm{dx}=\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{3}}…