Just Find Its Antiderivative Right?

Calculus Level 3

Evaluate the Riemann integral

011xdx. \int_0^1 \frac{1}{ \sqrt{x} } \, dx .


Note: The Riemann integral of ff equals SS if the following condition holds:

ϵ>0 \forall \epsilon > 0 , δ \exists \delta such that for any tagged partition x0,,xn x_0, \ldots , x_n and t0,,tn1 t_0, \ldots , t_{n-1} whose mesh is less than δ \delta , we have
i=0n1f(ti)(xi+1xi)S<ϵ. \left| \sum_{i=0}^{n-1} f(t_i) ( x_{i+1} - x_i) - S \right| < \epsilon.

Inspiration.

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