### 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.