First slide

Introduction to definite integration

Question

The value of
$lim_{n \to \infty} (\frac{1}{1^{3} + n^{3}} + \frac{2^{2}}{2^{3} + n^{3}} + \dots + \frac{n^{2}}{n^{3} + n^{3}})$ is

Easy

A

$\frac{1}{3}$
B

$\frac{1}{3} \log 2$
C

$\frac{1}{2}$
D

$\frac{1}{3} \log 3$

Solution

given limit= $\int_{0}^{1} \frac{x^{2}}{1 + x^{3}} d x = \frac{1}{3} \log (1 + x^{3}) \begin{array}{r} 1 \\ 0 \end{array} = \frac{1}{3} \log (2)\}$

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