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If $f (x) = lim_{n \to \infty} [2 x + 4 x^{3} + \dots + 2 {nx}^{2 n - 1}] (0 < x < 1)$ , then $\int f (x) dx$ is equal to

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Correct option is D

Let, gn(x)=1+x2+x4+…+x2n=x2n+2−1x2−1hn(x)=gn′(x)=2xnx2n+2−(n+1)x2n+1x2−12Now f(x)=limn→∞ hn(x)=2xx2−12As 0

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If f(x)=limn→∞ 2x+4x3+…+2nx2n−1(0<x<1), then ∫f(x)dx is equal to

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If $f (x) = lim_{n \to \infty} [2 x + 4 x^{3} + \dots + 2 {nx}^{2 n - 1}] (0 < x < 1)$ , then $\int f (x) dx$ is equal to