Category: Integration

Question Number 17506 by tawa tawa last updated on 06/Jul/17 $$\int {\tan }^{-1}\left(\sqrt{\frac{\mathrm{x}+1}{\mathrm{x}-1}}\right)\mathrm{dx}$$ Answered by sma3l2996 last updated on 06/Jul/17 $${u}={tan}^{−\mathrm{1}} \left(\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}}\right)\Rightarrow{u}'=\frac{−\mathrm{1}}{\mathrm{2}{x}\sqrt{\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)}}=\frac{−\mathrm{1}}{\mathrm{2}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}} \…

Question Number 148570 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}{\int }_0^{\mathrm{\infty }}\frac{\mathrm{logx}}{{\mathrm{x}}^2+\mathrm{x}+1}\mathrm{dx}$$ Answered by Ar Brandon last updated on 29/Jul/21…

Question Number 148566 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}{\mathrm{U}}_{\mathrm{n}}=\int {\int }_{[\frac{1}{\mathrm{n}},\mathrm{n}[}\frac{\cos ({\mathrm{x}}^2+{\mathrm{y}}^2)}{{\mathrm{x}}^2+{\mathrm{y}}^2}\mathrm{dxdy}$$$$\mathrm{and}\mathrm{determine}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}{\mathrm{U}}_{\mathrm{n}}$$$$\mathrm{nature}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} ? \…

Question Number 17479 by Arnab Maiti last updated on 06/Jul/17 $$\mathrm{If}f\left(x\right)\mathrm{is}\mathrm{a}\mathrm{periodic}\mathrm{function}\mathrm{with}\mathrm{period}$$$$\mathrm{time}\mathrm{t};\mathrm{prove}\mathrm{that}{\int }_{\mathrm{a}}^{\mathrm{a}+\mathrm{t}}f\left(x\right)\mathrm{d}x\mathrm{is}\mathrm{a}\mathrm{indipendent}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 17473 by Arnab Maiti last updated on 06/Jul/17 $$\mathrm{Prove}\mathrm{that}{\int }_0^{2\mathrm{a}}\sqrt{2\mathrm{ax}-{\mathrm{x}}^2}\mathrm{dx}=\frac{\mathrm{\Pi }{\mathrm{a}}^2}{2}$$ Answered by sma3l2996 last updated on 06/Jul/17 $${A}=\int_{\mathrm{0}}…