lim-n-0-1-x-n-1-x-n-1-n-dx-

Question Number 162287 by qaz last updated on 28/Dec/21

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}} +\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{n}} }\mathrm{dx}=? \\ $$

Commented by mr W last updated on 28/Dec/21

$${it}\:{should}\:{be}\:{equal}\:{to}\:\frac{\mathrm{3}}{\mathrm{4}},\:{geometrically}. \\ $$

Commented by MathsFan last updated on 28/Dec/21

$${yeah} \\ $$

Commented by mr W last updated on 28/Dec/21

Commented by qaz last updated on 28/Dec/21

$$\mathrm{yes}\:\mathrm{sir} \\ $$

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