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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 Inequality

An inequality involving integrals of squares of functions.

Integral Sandwich

Age 16 to 18 Challenge Level:
This is an example where you have to consider the cases of $n$ even and $n$ odd separately.

The general cases are proved exactly as for parts (i) and (ii) and you may find it easier to consider even values of $n$ first.