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Area L

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

Integral Equation

Solve this integral equation.

Integral Sandwich

Generalise this inequality involving integrals.

Integral Inequality

Age 16 to 18 Challenge Level:
Here the first part is a special case of the result in the second part. However it is easier to prove the general case directly.