Before you turn this problem in, make sure everything runs as expected. First, restart the kernel (in the menubar, select Kernel\(\rightarrow\)Restart) and then run all cells (in the menubar, select Cell\(\rightarrow\)Run All).

Make sure you fill in any place that says YOUR CODE HERE or “YOUR ANSWER HERE”, as well as your name and collaborators below:

Even and odd functions

An odd function \(o(x)\) satisfies \(o(x)=-o(-x)\) for all \(x\). Therefore, for any finite \(t\):

\(\int_{-t}^{t}o(x) dx=0\).

An even function \(e(x)\) satisfies \(e(x) = e(-x)\) for all \(x\). Therefore, for any \(t\):

\(\int_{-t}^{t}e(x) dx=2 \int_{0}^{t}e(x) dx\).

The complementary error function is defined by this integral:

\(erfc(x) = \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2} dt\)

determine if it is even or odd using both the criteria described above and using Python.

When you are done, download a PDF and turn it in on Canvas. Make sure to save your notebook, then run this cell and click on the download link.

%run ~/f23-06623/f23.py
%pdf