F(x) = et?: The Failure of Math 1B Math 1C We will spend the first half of this quarter studying infinite series, arguably the single most difficult concept in the Calculus sequence. To help us understand the need to develop this concept we will bring all of our Math 1B skills to bear on the indefinite integral
e^x^2dx
Integration by Parts Integration by Parts is considered by many mathematicians to be the single most useful tool in our integration toolkit. We will explore whether or not it can help with this indefinite integral.
a) Remembering that any function can be thought of as a function multiplied by the constant function 1, apply integration by parts to the integral one time. (5 points)
b) The resultant integral can also be tackled using integration by parts. I can think of 4 different ways you might separate the integral into the product of two functions. Try two of them. (10 points)
c) If you continued to apply integration by parts to this integral 5 times, without ever making a choice that would undo your work, what would you expect to end up with?