Limit and integration

Calculus Level 2

lim ⁡ n → ∞ ( 4 n ∫ 0 1 x n ( 1 − x ) n d x ) 1 n = a \large \lim_{n\to \infty} \left(4^n \int_{0}^{1} x^n \,(1-x)^n\,dx\right)^{\dfrac{1}{\sqrt{n}}} = a The value of the above expression is true for positive integer a a . Find the value of 2018 a 2018a .


The answer is 2018.

Naren Bhandari by Naren Bhandari , 21, India

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1 solution

Aaghaz Mahajan
May 7, 2018

Nice question...... @Naren Bhandari ........Simply use Beta Function along with Stirling's Approximation...

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