Post Edited Two Times: 9/3/2013
No question here. But if somebody sees something wrong, will post another question pertaining to specific rule:
Here is an easier way to do Simpson's rule without looking at a graph first:
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + 3i\Delta x) - 3\Delta x )]\).
\(\displaystyle \Delta x = \dfrac{b - a}{3n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
Also
Trapezoidal Rule
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + 2i\Delta x) - 2\Delta x )]\).
\(\displaystyle \Delta x = \dfrac{b - a}{2n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
Left Triangle Approximation
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + i\Delta x) - \Delta x )]\).
\(\displaystyle \Delta x = \dfrac{b - a}{n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
Right Triangle Approximation
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + i\Delta x]\).
\(\displaystyle \Delta x = \dfrac{b - a}{n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
Midpoint Triangle Approximation
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + i\Delta x) - \dfrac{1}{2}\Delta x)]\).
Correction
\(\displaystyle \Delta x = \dfrac{b - a}{n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
No question here. But if somebody sees something wrong, will post another question pertaining to specific rule:
Here is an easier way to do Simpson's rule without looking at a graph first:
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + 3i\Delta x) - 3\Delta x )]\).
\(\displaystyle \Delta x = \dfrac{b - a}{3n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
Also
Trapezoidal Rule
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + 2i\Delta x) - 2\Delta x )]\).
\(\displaystyle \Delta x = \dfrac{b - a}{2n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
Left Triangle Approximation
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + i\Delta x) - \Delta x )]\).
\(\displaystyle \Delta x = \dfrac{b - a}{n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
Right Triangle Approximation
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + i\Delta x]\).
\(\displaystyle \Delta x = \dfrac{b - a}{n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
Midpoint Triangle Approximation
Area = \(\displaystyle \sum_{i = 1}^{n} \Delta x[f((a + i\Delta x) - \dfrac{1}{2}\Delta x)]\).
Correction\(\displaystyle \Delta x = \dfrac{b - a}{n}\)
Interval: \(\displaystyle [a,b]\) or \(\displaystyle \int_{a}^{b}\)
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