This is a fairly standard exercise in integral calculus. I guess the standards for getting into Oxford to read mathematics is dropping.

Oh well. Anyway, can you figure out the right answer?

If so, perhaps you too, deserve a place at Oxford.

Solution

There’s a bit to unpack here. We have sketched the equation y = sqrt(x) and y = x – 2.

These two lines intersect at the point (4, 2). And the line y = x – 2 has x-intercept at 2.

Clearly, the area of the region we are after is the area of alpha + sigma – sigma. In other words, it’s the area under the curve y = sqrt(x) from 0 to 4 take away the area of the triangle sigma.

After computation, we should get 10/3 as the area of the region.