Numerical Integration Example using Trapezoids to approximate area

Estimate the area under the curve (x) = x² from x = 1 to x = 3

Note: This function happens to be an "increasing" function. (concave up)

Here Δx = (b – a)/2n

Note: The approximate area = ( y0 + 2y1 + 2y2 + 2y3 + y4 ) Δx

Here b = 3, a = 1, n = 4 so Δx = (3 – 1)/4 = 0.5

y0 = 1, y1 = 2.25, y2 = 4, y3= 6.25, and y4 = 9

Approximate area = ( 1.0 + 2x2.25 + 2x4 + 2x6.5 + 9 ) 0.25 = 8.875

Using trapezoids provides an improved approximation of the actual area.

Exact value of area = 26/3 = 8.66666

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