# Just Find Its Antiderivative Right?

Calculus Level 3

Evaluate the Riemann integral

$\int_0^1 \frac{1}{ \sqrt{x} } \, dx .$

Note: The Riemann integral of $$f$$ equals $$S$$ if the following condition holds:

For all $$\epsilon > 0$$, there exists a $$\delta$$ such that for any tagged partition $$x_0, \ldots , x_n$$ and $$t_0, \ldots , t_{n-1}$$ whose mesh is less than $$\delta$$, we have
$| \sum_{i=0}^n{n-1} f(t_i) ( x_{i+1} - x_i) - S | < \epsilon.$

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