Definite Integral

Calculus Level 3

lim ⁡ n → ∞ ∫ 0 2 π sin ⁡ ( n x ) x 2 + n 2 d x = ? \large \lim_{n\to\infty} \int_0^{2\pi} \dfrac{\sin(nx)}{x^2+n^2} \, dx = \, ?


The answer is 0.

Jose Sacramento by Jose Sacramento , 66, Portugal

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3 solutions

Just use sin(n(2π-x)) = sin(2πn-nx) = -sin(nx) = 0

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Jose Sacramento
May 3, 2017

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Aryan Mehra
May 2, 2017

The graph and limit of the question tends to 0. Moteover the integral can be verified to be zero by properties as well.

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