Category: Integration

Question Number 53477 by maxmathsup by imad last updated on 22/Jan/19 $$letf\left(a\right)={\int }_0^1\frac{dt}{\sqrt{x+a}+3}$$$$1)calculatef\left(a\right)$$$$2)findalso{\int }_0^1\frac{dt}{\sqrt{x+a}{(\sqrt{x+a}+3)}^2}$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\:\sqrt{{x}+\mathrm{1}}+\mathrm{3}}\:\:{and}\:\int_{\mathrm{0}}…

Question Number 53474 by maxmathsup by imad last updated on 22/Jan/19 $$calculate{\int }_0^1\frac{5^{2x+1}-2^{2x-1}}{{10}^x}dx$$ Answered by tanmay.chaudhury50@gmail.com last updated on…

Question Number 53471 by maxmathsup by imad last updated on 22/Jan/19 $$1)find{U}_n={\int }_0^{\frac{\pi }{4}}{tan}^{n}tdtwithnintegr.$$$$2)find{lim}_{n\to +\mathrm{\infty }}{U}_n$$$$3)calculate\sum _{n=0}^{\mathrm{\infty }}{U}_n$$$$…

Question Number 53467 by maxmathsup by imad last updated on 22/Jan/19 $$let{A}_{nm}={\int }_0^1{x}^n{(1-x)}^{m}dxwithnandnintegrsnaturals$$$$1)calculate{A}_{nm}byusingfactoriels$$$$2)find\sum _{n,m}{A}_{nm}$$…

Question Number 53463 by maxmathsup by imad last updated on 22/Jan/19 $$1)let0<\theta <\frac{\pi }{2}andA\left(\theta \right)={\int }_0^{\frac{\pi }{2}}\frac{dx}{\sqrt{x^2+2sin\theta x+1}}$$$$calculateA\left(\theta \right)$$$$2)calculate{\int }_0^{\frac{\pi }{2}}\frac{dx}{\sqrt{x^2+\sqrt{2}x+1}}$$ Commented…