9 FURTHER APPLICATIONS OF INTEGRATION

The Bizarre Coastline
3. As you probably expect, the island of Eerht is similar to the islands of Eno and Owt, except that the
northern border is given by y = sin 3x + 2. Please sketch Eerht, and compute its coastline and area.
Coastline Length of Eerht:
Area of Eerht:
4. Ah, if only we had the time to fully explore the islands of Ruof, Evif, and Xis... But there are a lot of
islands in this chain, and we don’t have all the time in the world. Let’s skip ahead a bit, and look at the
island of Net. Graph the northernmost border of Net (y = sin 10x + 2) on your calculator, and estimate
the length of the coastline of Net before computing.
Coastline Length of Net:
Area of Net:
5. You have probably noticed that there has been a pattern in the areas of this chain of islands, and the use
of this pattern will save us some in-person visits. Explain what you have observed, and show that your
conjecture holds for any one of the islands. What happens to the coastlines as we go farther along the
chain of islands?
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