Category: Integration

Question Number 33130 by prof Abdo imad last updated on 11/Apr/18 $$findthevalueof{\int }_0^{\mathrm{\infty }}\frac{1+xcos\theta }{x^2+2xcos\theta +1}dx.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 33125 by prof Abdo imad last updated on 10/Apr/18 $$letgive{u}_n={\int }_0^{\pi }\frac{cos\left(nx\right)dx}{1-2\lambda cosx+{\lambda }^2}$$$$1)provethat\lambda u_{n+2}-(1+{\lambda }^2)u_{n+1}+\lambda u_n=0$$$$\left.\mathrm{2}\right)\:{ptove}\:{that}\:\Sigma\:{u}_{{n}} \:{is}\:{convergent}\:{and}\:{find}\:{its}\:{sum}…

Question Number 33119 by abdo imad last updated on 10/Apr/18 $$find{\int }_0^{\mathrm{\infty }}\frac{t^n}{e^t-1}dtbyusing\xi \left(x\right)fornintegr$$$$\xi \left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{1}{n^x}withx>1.$$ Commented by prof…

Question Number 164162 by Zaynal last updated on 15/Jan/22 $$\mathrm{Prove}\mathrm{the};$$$$(\mathit{t}\mathit{a}\mathit{n}\mathit{\alpha }+\frac{\mathit{c}\mathit{o}\mathit{s}\mathit{\alpha }}{1+\mathit{s}\mathit{i}\mathit{n}\mathit{\alpha }})\mathit{s}\mathit{i}\mathit{n}\mathit{\alpha }=\mathit{\alpha }$$$${}^{[\mathrm{Z}.\mathrm{A}]}$$ Commented by som(math1967) last updated on 15/Jan/22 $$\left\{\boldsymbol{{tan}\alpha}\:+\frac{\boldsymbol{{cos}\alpha}\left(\mathrm{1}−\boldsymbol{{sin}\alpha}\right)}{\mathrm{1}−\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{\alpha}}\right\}×{sin}\alpha…

Question Number 33069 by abdo imad last updated on 09/Apr/18 $$byusingresidustheoremprovethat$$$${\int }_0^{\mathrm{\infty }}\frac{t^{a-1}}{1+t}dt=\frac{\pi }{sin\left(\pi a\right)}with0<a<1.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com