Calculate the area under $f(x) = \sqrt x$ on $[0,4]$ by computing the lower Riemann sum for $f$ with the given partition Where $x_i = \dfrac{4i^2}{n^2}$ and letting $n \rightarrow \infty$
I don't know how and where to begin.

$$
\sum_{i=0}^{n-1} f(x_i) \, \Delta x_i = \sum_{i=0}^{n-1} \sqrt{\frac{4i^2}{n^2}} \left( \frac{4(i+1)^2}{n^2} - \frac{4i^2}{n^2} \right).
$$
Etc.  Why don't you know where to begin?  Are you unaware of what Riemann sums are?  If so, maybe you could ask about that.
