(Solved): Using the definition of the definite intergral, write the definite intergral as the limit of a sum. ...

Using the definition of the definite intergral, write the definite intergral as the limit of a sum. The required information is below

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Using the definition of the definite integral, write the definite integral as the limit of a sum. The required information is below: \( f(x)=x^{2} \), from \( x=0 \) to \( x=3 \) \[ \begin{array}{r} \lim _{n \rightarrow \infty}\left(\sum_{i=1}^{n} f\left(\frac{1}{n} i\right) \frac{1}{n}\right) \\ \lim _{n \rightarrow \infty}\left(\sum_{i=1}^{n} f\left(\frac{2}{n} i\right) \frac{2}{n}\right) \\ \lim _{n \rightarrow \infty}\left(\sum_{i=1}^{n} f\left(\frac{3}{n} i\right) \frac{3}{n}\right) \\ \lim _{n \rightarrow \infty}\left(\sum_{i=1}^{n} f\left(\frac{3}{n} i\right)\right) \end{array} \]