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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:
A differential equation involves functions and derivatives. Integral equations involve functions and integrals.

In this example you have an integral equation. First you have to differentiate both sides. Then you have to solve a differential equation where you should be able to spot the solution immediately. Then you have to check that you have found a solution by substituting the function you have found into the integral equation.