Find max value of int [0,1] [f(x)]^3 dx given -1 <= f <= 1 for all x, and...

patssquad

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find the maximum value of integral 0 to 1 of [f(x)]^3 dx given -1 is less than or equal to f(x) is less than or equal to 1 for all x, and integral from 0 to 1 of f(x)dx is 0 Can you please show work? and explain how to do the problem

. . .\(\displaystyle \displaystyle \int_0^1\, \left[f(x)\right]^3\, dx\)

. . .\(\displaystyle \displaystyle \int_0^1\, f(x) \, dx\, =\, 0\)
 

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