Numerical Integration Example using Right 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 = ( y1 + y2 + y3 + y4 ) Δx

Further Note: In this application use of the right end sampling point will result

in an overestimation of the actual area.

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

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

Approximate area = ( 2.25 + 4 + 6.5 + 9 ) 0.5 = 10.875

Actual value of area = 8.66666

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