Practice Problems: Riemann Sums

The Left-Hand Rule (LHR) is a rudimentary numerical integration technique for approximating the area under the curve. The height for each rectangular region is \(f(x_k)\) where \(x_k\) is the left-hand endpoint on the interval, thus, the reason behind the mystery why this rule is known as the Left-Hand Rule.

The Right-Hand Rule (RHR) is another rudimentary numerical integration technique for approximating the area under the curve. The height for each rectangular region is \(f(x_{k+1})\) where \(x_{k+1}\) is the right-hand endpoint on the interval.

\(\displaystyle\texttt{LHR Area}\approx \sum_{k=0}^{n-1}f(x_k)\Delta x\) AND \(\displaystyle\texttt{RHR Area}\approx\sum_{k=1}^{n}f(x_k)\Delta x\)

where \(x_k=a+k\Delta x\) for \(k=0,1,2,\dots,n\). Notice that \(a=x_0\) and \(b=x_n\)

Virtual Lessons

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