Category: Integration

Question Number 40044 by abdo mathsup 649 cc last updated on 15/Jul/18 $$letf\left(t\right)={\int }_0^{\frac{\pi }{2}}ln(cosx+tsinx)$$$$1)calculatef\left(0\right)$$$$2)calculate{f}^{{}^{\prime }}\left(t\right)thenfindasimpleformoff\left(t\right)$$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cosx}\:+\mathrm{2}\:{sinx}\right){dx} \…

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}}…

Question Number 105565 by mathmax by abdo last updated on 30/Jul/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^2\ln (1-{\mathrm{x}}^3)$$$$1)\mathrm{calculate}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(0\right)$$$$2)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$$$3)\mathrm{calculate}\int \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$$ Answered…

Question Number 171090 by Kodjo last updated on 07/Jun/22 $$I_n={\int }_0^1(1-u)\sqrt{ud\left(u\right)}$$$$Demonstratethat\mathrm{\forall }n\in N,I_{n+1}-I_n={(1-u)}^n{u}^{\frac{3}{2}}d\left(u\right)anddeducethemeaningofvariationsof\left(I_n\right)\in N$$ Commented by Kodjo…

Question Number 40008 by math khazana by abdo last updated on 15/Jul/18 $$1)find\int \frac{dx}{(x+1)\sqrt{x}+x\sqrt{x+1}}.$$ Commented by abdo mathsup 649 cc last updated on 15/Jul/18…