Category: Integration

Question Number 34222 by abdo imad last updated on 03/May/18 $$letgivethesequenceofintegrals$$$$J_n={\int }_0^{\mathrm{\infty }}{x}^n{e}^{-\frac{x^2}{2}}dx$$$$1)provethat{J}_n=(n-1)J_{n-2}\mathrm{\forall }n⩾2$$$$\left.\mathrm{2}\right)\:{calculate}\:{J}_{\mathrm{2}{p}}…

Question Number 34220 by abdo imad last updated on 03/May/18 $$calculateI={\int }_0^{\frac{\pi }{4}}cosxln\left(tanx\right)dx.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 34218 by abdo imad last updated on 02/May/18 $$find\int \sqrt{tanx}dx$$$$2)calculate{\int }_0^{\frac{\pi }{6}}\sqrt{tanx}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 34216 by abdo imad last updated on 02/May/18 $$letgiveI={\int }_0^1\frac{ln(x+1)}{x}dxandJ={\int }_0^1\frac{ln(1-x)}{x}dx$$$$1)provetheexistenceofIandJ$$$$2)calculateI+Jand2I+J$$$$3)findIandJ.$$ Terms of…

Question Number 165271 by mnjuly1970 last updated on 28/Jan/22 $$$$$$\mathrm{L}et,f:[0,1]\to \mathbb{R}isacontinuous$$$$function,provethat:$$$${lim}_{n\to \mathrm{\infty }}{\int }_0^1\frac{nf\left(x\right)}{1+n^2{x}^2}dx=\frac{\pi }{2}f\left(0\right)$$$$---proof---$$$$\:\:\:\:\:\:\:\:\:\mathrm{S}_{\:{n}}…