Answer to Question #113083 in Calculus for Sourav Mondal

Question #113083
Let P = {0,1/4,1/2,3/4,1} be a partition of [0, 1]
and a function f : [0, 1] —> R be defined by
f(x) = x³ . Find U(P, f).
1
Expert's answer
2020-04-30T19:24:43-0400

Given P = [0, 1/4, 1/2, 3/4, 1]. So δx=1/4\delta x = 1/4 .

U(P,f) = [f(14)+f(12)+f(34)+f(1)].δx=[(1/4)3+(1/2)3+(3/4)3+13](14)[ f(\frac{1}{4})+f(\frac{1}{2})+f(\frac{3}{4})+f(1)].\delta x = [(1/4)^3 + (1/2)^3+(3/4)^3+1^3] (\frac{1}{4})

= 1.5625/4 = 0.390625.


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