Area L

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

Integral Sandwich

Generalise this inequality involving integrals.

Integral Inequality

An inequality involving integrals of squares of functions.

Integral Equation

Age 16 to 18 Challenge Level:

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