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use a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating the f at the subinterval midpoints.


f(x)=x^4 on [0,2]

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nobillionaireNobley

Four partitions = 0 - 0.5, 0.5 - 1, 1 - 1.5, 1.5 - 2
Midpoints = 0.25, 0.75, 1.25, 1.75
Required sum = 0.5(0.25^4 + 0.75^4 + 1.25^4 + 1.75^4)/(2 - 0) = 0.5(0.00390625 + 0.31640625 + 2.44140625 + 9.37890625)/2 = 0.25(12.140625) = 3.03515625

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