$\mathop {\lim }\limits_{n \to \infty } \,\,\mathop \sum \limits_{r = 1}^n \,\,\left| {\,\frac{{{r^3}}}{{{r^4}\,\, + \,\,{n^4}}}\,} \right|$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\lim\limits_{n \to \infty } \,\,\sum \limits_{r = 1}^n \,\,\left| {\,\frac{{{r^3}}}{{{r^4}\,\, + \,\,{n^4}}}\,} \right|

equals

View answer and explanation

Correct option: D

\frac{1}{4}\,\,\log \,\,2

Option D (

\frac{1}{4}\,\log \,2

) is correct because the limit of the Riemann sum can be expressed as a definite integral, which evaluates to

\frac{1}{4}\,\log \,2

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