Calculus Level 3

An infinitely thin, \(k\text{ cm}\)-long squeegee begins to slide down from the upper-left corner of a \(k\text{ cm} \times k\text{ cm}\) 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 \(k=\sqrt{\dfrac{2016}{\pi }}\), what is the area of the window \(\big(\)in \(\text{cm}^2\big)\) 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


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