Calculus Level 3

An infinitely thin, k cmk\text{ cm}-long squeegee begins to slide down from the upper-left corner of a k cm×k cmk\text{ cm} \times k\text{ cm} square window. Its other end simultaneously slides toward the lower-right corner of the window, with the upper end kept in contact with the left side of the window.

If k=2016πk=\sqrt{\dfrac{2016}{\pi }}, what is the area of the window (\big(in cm2)\text{cm}^2\big) cleaned by the squeegee?

Note: you may end up with an integral expression that's difficult to evaluate analytically. Feel free to finish the job using the code environment below:

import math
Python 3
You need to be connected to run code


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