Oxford MAT

Are You Smart Enough For A Math Degree at Oxford University?

A math problem with a simple solution!

The beauty of mathematics sometimes lies in its simplicity, in that a seemingly complex problem can be broken down if we stick to the basics.

And we are going to see just that in today’s puzzle from Oxford University’s entrance exam for math degrees. 👩‍🎓

Here’s a hint: think about the nature of each function …

I recommend you pause the article, grab your pen and paper, and give this a go. When you are ready, keep reading for the solution! ✒️

Solution

This is a product of three definite integrals. The essence of this problem is to evaluate whether each individual integral is zero, positive, negative or undefined.

First Integral

Let us look at the first one.

What do you think the graph looks like? Recall that the cosine graph is symmetrical along the y-axis.