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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