Numerical Integration Example using Trapezoids to approximate area
Estimate the area under the curve y(x) = x2 from x = 1 to x = 3 .
Note: This function happens to be an "increasing" function. (concave up)
Here Δx = (b – a)/n
Note: The approximate area = ( y0 + 2y1 + 2y2 + 2y3 + y4 ) (Δx/2)
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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