Answer
$\frac{2000000}{3}$
Work Step by Step
$$\sum_{i=1}^{n}\sqrt{i}=\sum_{i=1}^{n}\sqrt{0+1\cdot i}\cdot 1=\sum_{i=1}^{n}\sqrt{x_i}\cdot 1$$
$\frac{b-a}{n}=1$, $a=0$ $\to $ $b=n$ so for $n=10000$ the value of $b=10000$:
$$\sum_{i=1}^{10000}\sqrt{i}=\lim_{n \to 10000}\sum_{i=1}^{n}\sqrt{i}=\int_0^{10000}\sqrt{x}dx=\frac{2000000}{3}$$
