Limits in an integral

Calculus Level 3

lim ⁡ n → ∞ ∫ 0 1 cos ⁡ x n d x \large \lim_{n\to\infty} \int_0^1 \cos \sqrt[n] x \, dx

If the limit above is in the form of cos ⁡ a \cos a , find the minimum possible value of a a .


The answer is 1.

Hamza A by Hamza A , 19, USA

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1 solution

Hamza A
Feb 16, 2016

simple, x n \sqrt [ n ]{ x } tends to 1 as n tends to infinity,this will be a rectangle of height cos ⁡ 1 \cos{1} and width 1 since the integral is from 0 to 1

so a = 1 a=1

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