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

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

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NRICH is part of the family of activities in the Millennium Mathematics Project.

NRICH is part of the family of activities in the Millennium Mathematics Project.