Calculate the Riemann sum $R(f,p,c)$ for the function $f(x)=3x^2+2x$.
Partition $p={0,1,2.5,3.2,5}$ and sample points $c={0.5,2,3,4.5}$.
Am able to find a Riemann sum whereby partitions have been given. In this case, am wondering were the sample points are to be used in calculation.
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$\begingroup$For the partition $0,1,2.5,3.2,5$ and sample points $0.5,2,3,4.5$, the Riemann sum is $$ f(0.5) \;\cdot\big( 1-0\big) +f(2)\;\cdot\big( 2.5-1\big) +f(3)\;\cdot\big( 3.2-2.5\big) +f(4.5)\;\cdot\big( 5-3.2\big) $$
[Note: the edit of $4.5$ into $4,5$ was incorrect. This partition has four intervals, so we need four sample points.]
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