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 156194 by talminator2856791 last updated on 09/Oct/21

$$$$$${\int }_0^1\sqrt{x\sqrt{x^2\sqrt{x^3.....\sqrt{x^n}}}}dx$$$$n\in \mathbb{N}$$$$$$

Commented by MJS_new last updated on 10/Oct/21

$$=\underset{0}{\stackrel{1}{\int }}{x}^{2-\frac{n+2}{2^n}}dx={\left[\frac{x^{3-\frac{n+2}{2^n}}}{3-\frac{n+2}{2^n}}\right]}_0^1=\frac{2^n}{3\times 2^n-n-2}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com