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A TMUA Math Problem

The absolute value function does not have follow any elementary integration rules. We can however bypass this by considering its graph.

This fun integral challenge comes from TMUA, a test by Cambridge University for students looking to study Computer Science at the university 💻

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

The trickiest part about this problem is the absolute value function |x|.

What we will do is to split the integral into two, first integrating from x = -1 to x = 0, then from x = 0 to x = 3.

Since the values are negative in the first integral, |x| = -x.

Equally the values are positive in the second integral, so |x| = x.

We then expand the brackets

Now I trust that you are capable of integrating using reverse power rule.

And you should get the following!

And that's our answer.

How amazing 🐉

What was your thought process this time? Comment down below, I am eager to know :) 🏹

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