Numerical Integration Example using Left Endpoint
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)
Note: The approximate area = ( y0 + y1 + y2 + y3 ) Δx
Further Note: In this application use of the right end sampling point will result
in an underestimation of the actual area.
Here b = 3, a = 1, n = 4 so Δx = (3 – 1)/4 = 0.5
y0 = 1, y1 = 2.25, y2 = 4, and y3= 6.25
Approximate area = ( 1.0 + 2.25 + 4 + 6.5 ) 0.5 = 6.75
Exact value of area = 26/3 = 8.66666
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