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A Basic Approach

20 January, 2016 - 09:21
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There are various methods to calculating the area under a curve, for example, Rectangle Method 1, Trapezoidal Rule 2 and Simpson’s Rule 3The following procedure is a simplified method.

Consider the curve below:

media/image2.png
Figure 6.1 Numerical integration 

Each segment under the curve can be calculated as follows:

\frac{1}{2}\left ( y0+y1 \right )\Delta x+\frac{1}{2}\left ( y1+y2 \right )\Delta x +\frac{1}{2}\left ( |y2+y3 \right )

Therefore, if we take the sum of the area of each trapezoid, given the limits, we calculate the total area under a curve. Consider the following example.

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