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Area L

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

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Integral Equation

Solve this integral equation.

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Integral Inequality

An inequality involving integrals of squares of functions.

Integral Sandwich

Age 16 to 18 Challenge Level:
You might find it useful to sketch a graph. The graph of $f(x)$ can take any shape but the inequalities tell you it is sandwiched between the axes and some other graph, so you can deduce something about the area under the graph of $f(x)$ and hence about the integral.