Finding the limit of a sequence of integrals – math.stackexchange.com

Finding the limit of a sequence of integrals – math.stackexchange.com

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Let us define a sequence of function as $$f_n(x)=\frac{2nx^{n-1}}{x+1}\;\;\text{for each $x\in [0,1]$ and for all $n\in\mathbb{N}$}$$ What is $\displaystyle \lim_{n\to \infty} \int_0^1 f_ n(x) dx$ ...

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