Calculus Level 5

An elf finds himself in a random place in a square field that is $$2\text{ km}$$ by $$2 \text{ km}$$. Right in the centre of the field is the present factory, which can be assumed to be a point.

He needs to return to the factory promptly, so he does so by walking in a straight line back to the factory (the shortest distance).

Find the root mean square average of the length of his journey, and give your answer to the nearest metre.

Note: The root mean square is also known as the quadratic mean.

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