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