JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\lim \limits_{{n \rightarrow \infty}} \frac{1}{n} \sum\limits_{{r=1}}^{2 n} \frac{r}{\sqrt{n^2+r^2}}

equals

View answer and explanation

Correct option: B

\sqrt{5}-1

Option D (

\sqrt{5}-1

) is correct because the limit of the Riemann sum converts to the integral

\int_0^2 \frac{x}{\sqrt{1+x^2}} dx

, which evaluates to

\sqrt{5}-1

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