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Solve this integral equation.

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Generalise this inequality involving integrals.

Integral Inequality

An inequality involving integrals of squares of functions.

Area L

Age 16 to 18 Challenge Level:

Start by drawing a sketch of the graph of $f(x)$ for $a\leq x \leq b$.
What is represented by $bf(b) - af(a)$?
Which parts of the graph correspond to the integrals?