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Suppose $f(x)>0$ for all $x$ in $[0,10]$. Express the area under the curve $f(x) $for $0≤x≤10$ as the limit of a sum, using the value of $f(x)$ at right endpoints of your intervals.

Could you explain how to solve it?

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up vote 3 down vote accepted

Your functions $f$ is positive everywhere on $[0,10]$. By definition, the area under the $f$ on the interval $[0,10]$ is

$$ \int\limits_0^{10} f dx = \lim_{ n \to \infty } \sum_{i=1}^n f( \frac{10i}{n}) \frac{10}{n} $$

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Are you using right Riemann sum? if so, then $i$ should be from $1$ to $n$. – Mhenni Benghorbal Dec 4 '13 at 8:59
    
corrected...... – ILoveMath Dec 4 '13 at 9:02

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