Discover the Path to Mathematical Mastery
An Education That Counts
Discover the Path to Mathematical Mastery
An Education That Counts
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 \(b=x_n\)Need some additional help understanding how to apply this integration technique? Click Here to visit the virtual lesson section.
Answer the following questions by using Riemann Sums.
Determine the function \(f(x)\) over a given interval \((a,b)\) that leads to the given Riemann Sum