Category: Integration

Question Number 133214 by mathmax by abdo last updated on 20/Feb/21 $$\mathrm{calculate}\mathrm{f}\left(\xi \right)={\int }_0^{\mathrm{\infty }}\frac{\mathrm{x}\sin \left(\xi \mathrm{x}\right)}{1+{\mathrm{x}}^4}\mathrm{dx}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 67674 by Abdo msup. last updated on 30/Aug/19 $$letf\left(a\right)={\int }_0^{\mathrm{\infty }}\frac{dx}{(x^2+1)(x^2+a)}witha>0$$$$1)determineaexplicitformoff\left(a\right)$$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+{a}\right)^{\mathrm{2}} } \…

Question Number 133187 by mnjuly1970 last updated on 19/Feb/21 $$\dots \dots .CALCULUS\dots \dots$$$$lim{}_{n\to \mathrm{\infty }}\left(n(ln\left(2\right)-\underset{k=1}{\sum ^n}\frac{1}{n+k})\right)=?$$$$$$ Terms of Service Privacy Policy Contact:…

Question Number 133173 by john_santu last updated on 19/Feb/21 $${\int }_0^{\frac{1}{2}}\sqrt{1+\sqrt{1-{\mathrm{x}}^2}}\mathrm{dx}=?$$ Answered by EDWIN88 last updated on 19/Feb/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \sqrt{\mathrm{1}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…

Question Number 2088 by Yozzi last updated on 01/Nov/15 $$Showthat\mathrm{\forall }n\in {\mathbb{Z}}^{+}$$$${\int }_0^{\pi /4}{tan}^{2n+1}\theta d\theta ={(-1)}^n(\frac{1}{2}ln2+\underset{m=1}{\sum ^n}\frac{{(-1)}^m}{2m}).$$$${Deduce}\:{that}\:\underset{\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}−\mathrm{1}} }{\mathrm{2}{m}}=\mathrm{0}.\mathrm{5}{ln}\mathrm{2}. \…