Riemann Sum as a Definite Integral

Question

Which of the following definite integrals is equal to $$\displaystyle\lim_{n 	o \infty} \frac{2}{n} \sum_{k=1}^{n} \ln\left(1 + \frac{2k}{n}ight)$$?

Accepted Answer

$$\displaystyle\int_1^3 \ln(x) \, dx$$

Answer

$$\displaystyle\int_0^2 \frac{1}{1 + x} \, dx$$

Answer

$$\displaystyle\int_0^1 \ln(1 + 2x) \, dx$$

Answer

$$\displaystyle\int_0^1 \ln(1 + x) \, dx$$

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