Answer:
The given expression is:
[tex]\lim_{n \to \infty} \sum x_{i}ln(2x+x_{i} ^{2}) \Delta x[/tex]
This expressions represent the sum of certain numbers of rectangles that comprehend the area under a curve, where the number of rectangles tend to infinite. Actually, this definition states that when [tex]n[/tex] tend to infinite, there's the area under the curve.
However, this can be expresses as a definite integral, which tend to have more sense for students:
[tex]\int\limits^3_0 {xln(2+x^{2})} \, dx[/tex]
With the integral form can be shown better what we tried to say before. The integral represents the area under the given function [tex]xln(2+x^{2})[/tex], but just the part inside the interval from 0 to 3. The limit also refers to this, but in a different notation.
