9 FURTHER APPLICATIONS OF INTEGRATION
9 FURTHER APPLICATIONS OF INTEGRATION
9 FURTHER APPLICATIONS OF INTEGRATION
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The Bizarre Coastline<br />
6. For our final stop, let’s go to the mysterious and oft-misunderstood island of Ytinifni. This island is not<br />
in the same chain as the others; it is where the inhabitants of the other islands go for their vacations. Its<br />
( ) 1<br />
northern border is given by y = (x − π) sin + 2. Try your best to sketch this mysterious island.<br />
x − π<br />
Notice that it is very hard to draw. There is a legend of a hole in the middle of the northern border that<br />
will claim the life of any tourist who sets foot there. (I’ve been to that area, and seen nothing unusual —<br />
why do you think that is?) Now, using geometric reasoning or numerical approximation, complete the<br />
following:<br />
Coastline Length of Ytinifni:<br />
Area of Ytinifni:<br />
7. Is this result counterintuitive? Try to explain it, and ask your teacher for help if you cannot do so.<br />
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