- #1

- 55

- 0

## Homework Statement

Find the first three nonzero terms in the power series representation in powers of x (ie. the maclaurin series for: (the equation in the latex image below)

## Homework Equations

fundamental theorem of calculus,

e^x = sum from n=0 to infinity of x^n/n!

## The Attempt at a Solution

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21f%28x%29%20%3D%20%5Cint_0%5Ex%20t%5E2exp%7B-t%5E2%7Ddt%20%20%20%20%5C%5Cf%27%28x%29%20%3D%20%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B%28-1%29%5En%20x%5E%7B2n%2B2%7D%7D%7Bn%21%7D%20%5C%5Cf%28x%29%20%3D%20%5Cint%20%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B%28-1%29%5En%20x%5E%7B2n%2B2%7D%7D%7Bn%21%7Ddx%20%5C%5C%20f%28x%29%20%3D%20C%20%2B%20%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B%28-1%29%5En%20x%5E%7B2n%2B3%7D%7D%7B%282n%2B3%29%20n%21%7D.gif [Broken]

Which gives 1/3 - (x^5)/5 + (x^7)/14 as the first three non zero terms.

I guess my question is i'm very unsure if you can actually do this or if you have to grind through a painful amount of derivatives to get the answer. Also, the presence of the Constant after you 'reintegrate' the power series confuses me. Is it not needed because there is an integral on the other side of the equation or am I doing something wrong by ignoring it.

Last edited by a moderator: