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
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.