#integral of single var

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grim dew
#

Let ( f(x) ) be a function with a second derivative on the interval ([0, a]) ((a > 0)), and suppose that ( f(x) > 0 ) and ( f''(x) > 0 ). Prove that:

[
\int_{0}^{a} f(x) , dx > a f\left(\frac{a}{2}\right).
]

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