Category: Integration

Question Number 25682 by abdo imad last updated on 13/Dec/17 $$wegive{\int }_0^{\mathrm{\infty }}{t}^{a-1}{(1+t)}^{-1}dt=\pi {\left(sin\left(\pi a\right)\right)}^{-1}with0<a<1findthevalueof{\int }_0^{\mathrm{\infty }}{(1+x^{16})}^{-1}dx$$ Answered by ajfour…

Question Number 91217 by mhmd last updated on 28/Apr/20 Commented by Prithwish Sen 1 last updated on 28/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{n}\pi} \mid\mathrm{cosx}\mid\mathrm{dx}\:=\:\boldsymbol{\mathrm{n}}\int_{\mathrm{0}} ^{\boldsymbol{\pi}} \mid\mathrm{cosx}\mid\mathrm{dx}\:=\:\mathrm{n}\left[\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{\mathrm{cosxdx}}+\int_{\frac{\boldsymbol{\pi}}{\mathrm{2}}}…

Question Number 25677 by abdo imad last updated on 12/Dec/17 $$let0<x<1findthevalueofF\left(x\right)=\int \ln (1+xcost)dtfromt=0tot=pi$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 156739 by cortano last updated on 15/Oct/21 Commented by john_santu last updated on 15/Oct/21 $$B=\int \sqrt{\frac{\sin x+\cos x}{\sin x-\cos x}}dx$$$$=\int \sqrt{\frac{\sin (x+\frac{\pi }{4})}{-\cos (x+\frac{\pi }{4})}}dx$$$$=\int \sqrt{-\tan (x+\frac{\pi }{4})}dx$$$$=\int \sqrt{\cot (x+\frac{3\pi }{4})}d(x+\frac{3\pi }{4})$$$$\:=\int\:\frac{{dq}}{\:\sqrt{\mathrm{tan}\:{q}}}\:…

Question Number 91183 by I want to learn more last updated on 28/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com