# Maclaurin Polynomials of integrals - Help needed

1. Oct 23, 2012

### chief10

Now i'm trying to get my head around this question. I just know they're going to give us a large degree question like this in the exam...

Let's say:

I = ∫[e^(x^2)]dx with nodes being x=0 to x=0.5

The 5th degree polynomial is 1 + x^2 + (1/2)(x^4)

So my queries are:

How would I go about finding the upper bound on the error from 0 to 0.5? - My working gives 0.012
How do I get an approximation of I by integrating? - my working gives 0.545
How would I get an upper bound on the integration in the previous question?

Thanks a lot guys and girls.

Last edited: Oct 23, 2012
2. Oct 23, 2012

### Staff: Mentor

This is incorrect. The first few terms of the Maclaurin series for et are 1 + t + t2/2! + t3/3! + t4/4! + ...

If you replace t by x2, what do you get?

3. Oct 23, 2012

### chief10

i was working under this assumption:

P(x) = f(a) + f'(a)(x-a) + [f''(a)(x-a)^2]/2! + ....etc..

where a=0 for Maclaurin

hmm

4. Oct 23, 2012

### chief10

alright going by that i've computed which i double checked with the taylor series for a=0

1 + x^2 + (1/2)(x^4)

any ideas on the rest?

Last edited: Oct 23, 2012
5. Oct 23, 2012

### HallsofIvy

So integrate! You know how to integrate that, don't you?

6. Oct 23, 2012

### chief10

no need to snap at me.. lol.. of course i do - look at my markings next to the bolded questions

i just thought i could get some insight and to see if i was doing it correctly