Category: Integration

Question Number 10495 by ajfour last updated on 14/Feb/17 $${\int }_0^{2\pi }\sqrt{R^2+r^2-2Rr\cos \theta }d\theta$$ Answered by robocop last updated on 14/Feb/17 $${todo}\:{en}\:{funcion}\:{de}\:\theta \…

Question Number 76014 by Master last updated on 22/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 10469 by FilupSmith last updated on 11/Feb/17 $$\mathrm{One}\mathrm{definition}\mathrm{of}\mathrm{\Gamma }(x+1)\mathrm{is}:$$$$\mathrm{\Gamma }(x+1)={\int }_0^{\mathrm{\infty }}{e}^{-t}{t}^{x}dx$$$$$$$$\mathrm{According}\mathrm{to}\mathrm{WolframAlpha},\mathrm{another}$$$$\mathrm{definition}\mathrm{is}:$$$$\Gamma\left({x}+\mathrm{1}\right)=\frac{\mathrm{1}}{{e}^{\mathrm{2}{i}\pi{x}} −\mathrm{1}}\oint_{{L}}…

Question Number 141532 by sarkor last updated on 20/May/21 Answered by qaz last updated on 20/May/21 $$\int \frac{3\sin x-2\cos x}{1+\cos x}dx$$$$=\int \frac{6\sin \frac{x}{2}\cos \frac{x}{2}-4\cos {}^2\frac{x}{2}+2}{2\cos {}^2\frac{x}{2}}dx$$$$=\int\left(\mathrm{3tan}\:\frac{{x}}{\mathrm{2}}−\mathrm{2}+\mathrm{sec}\:^{\mathrm{2}} \frac{{x}}{\mathrm{2}}\right){dx} \…

Question Number 141534 by sarkor last updated on 20/May/21 Answered by som(math1967) last updated on 20/May/21 $$\int {\mathit{c}\mathit{o}\mathit{s}}^2{\mathit{x}\mathit{s}\mathit{i}\mathit{n}}^8\mathit{x}\mathit{c}\mathit{o}\mathit{s}\mathit{x}\mathit{d}\mathit{x}$$$$=\int (1-{\mathit{s}\mathit{i}\mathit{n}}^2\mathit{x}){\mathit{s}\mathit{i}\mathit{n}}^8\mathit{x}\mathit{d}\left(\mathit{s}\mathit{i}\mathit{n}\mathit{x}\right)$$$$=\int\boldsymbol{{sin}}^{\mathrm{8}}…