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Today's calculation of Integral 876

Source:

May 16, 2013
calculusintegrationfunctioncalculus computationsfunctionsDefinite integral

Problem Statement

Suppose a function f(x)f(x) is continuous on [−1, 1][-1,\ 1] and satisfies the condition :
1) f(−1)≥f(1).f(-1)\geq f(1).
2) x+f(x)x+f(x) is non decreasing function.
3) ∫−11f(x) dx=0.\int_{-1}^ 1 f(x)\ dx=0.
Show that ∫−11f(x)2dx≤23.\int_{-1}^1 f(x)^2dx\leq \frac 23.
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