3) Assume that equals its Maclaurin series for all x.
Use the Maclaurin series for to evaluate the integral. Your answer will be an infinite series. Use the first two terms to estimate its value.
I am not sure how to do this!
Now this does not fit exactly what I have found, namely , but that's not particularly surprising because the next term in the series gives .
So at that time, my teacher was simply testing whether I had found the solution to this exercise on my own (or at least understood the solution so well that I was able to argue for it convincingly). If a student gets the solution from someone else however, he or she typically will not immediately try to argue for its correctness, but instead rather quickly withdraw...