Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 34910 by abdo imad last updated on 12/May/18

$$find{J}_{n,p}={\int }_0^{\mathrm{\infty }}{x}^n{e}^{-\frac{x^2}{p}}dxwithp>0andnintegr$$

Commented by candre last updated on 13/May/18

$$u=x^{n-1}\Rightarrow du=(n-1)x^{n-2}dx$$$$dv={xe}^{-\frac{x^2}{p}}dx\Rightarrow v=\int {xe}^{-\frac{x^2}{p}}dx$$$$w=-\frac{x^2}{p}\Rightarrow dw=-\frac{2x}{p}dx$$$$v=-\frac{p}{2}\int e^{w}dw=-\frac{p}{2}{e}^{-\frac{x^2}{p}}$$$$\underset{0}{\stackrel{\mathrm{\infty }}{\int }}{x}^n{e}^{-\frac{x^2}{p}}dx=-{\left[\frac{{px}^{n-1}{e}^{-\frac{x^2}{p}}}{2}\right]}_0^{\mathrm{\infty }}+\frac{(n-1)p}{2}\underset{0}{\stackrel{\mathrm{\infty }}{\int }}{x}^{n-2}{e}^{-\frac{x^2}{p}}dx$$$$J_{n,p}=\frac{(n-1){pJ}_{n-2,p}}{2}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com