### 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:
The first part of this question involves an easy evaluation of the integrals and then some simple algebra to compare the results.

In the second part you will get a quadratic inequality in $\lambda$ of the form $$U + 2V\lambda + W\lambda^2 \geq 0.$$ Completing the square leads to a condition for this inequality to hold which gives the required result.