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

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Generalise this inequality involving integrals.

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Integral Equation

Stage: 5 Challenge Level: Challenge Level:1

Solve the following integral equation for $f(x)$: $$\int_0^x f(t)\,dt = 3f(x)+k\,,$$ where $k$ is a constant.