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HELP! 1st Yr Uni: Series + Integrating?

Ok so basically, Ive been set work on stuff we haven't even covered in lectures, and my text book is no help so I have no idea where to start!
I don't want an answer, but if someone could talk me through the steps I need to take that would be brilliant! Heres the first question and i'm hoping I should be able to attempt the rest if I can get help with this one!

Thanks!

Use series and a calculator to evaluate

\int e^{-x^2}

as accurately as your calculator will allow.

EDIT Been a while since i've been on here so obviously my latex aint good!

Its the integral of e^{-x^2}

Reply 1

DoMakeSayThink

Sounds like you may want to look up some methods of quadrature.

http://en.wikipedia.org/wiki/Numerical_integration might be a start.

Reply 2

clear.twilight

I can do the normal integrating then evaluating with calculator, but I dont know where to start on series?

I know the taylor series for e^x so do i just replace the x in that formula with -x^2? Then integrate that... But then what do i do...? :s-smilie:

Im so confused!

Reply 3

jonny23563

Do you know the series that gives e? Have a look here.

Reply 4

Linda and Suzanne

clear.twilight

I know the taylor series for e^x so do i just replace the x in that formula with -x^2? Then integrate that... But then what do i do...? :s-smilie:

Im so confused!

Yes. Then what do you do? Give yourself a treat!

Reply 5

clear.twilight

So i'll have series from n= 0 to infinity of (-x^2)^n all over n! What on earth do I do with that? :s-smilie:

Reply 6

DFranklin

What are the limits you have been asked to integrate between?

Reply 7

clear.twilight

Oh yes sorry 0 and 0.1

Reply 8

Oh I Really Don't Care

clear.twilight

So i'll have series from n= 0 to infinity of (-x^2)^n all over n! What on earth do I do with that? :s-smilie:

Consider the first [as a rough] estimate the four terms that start the series and integrate these individually

Reply 9

clear.twilight

Do I need to use the limits 0 and 0.1 for anything to do with the series? Or so i just use n=0,1,2,3?

Reply 10

Oh I Really Don't Care

clear.twilight

Do I need to use the limits 0 and 0.1 for anything to do with the series? Or so i just use n=0,1,2,3?

i.e. Taylor series for e^x = 1 + x + x^2/2! + x^3/3! ... + x^n/n!

Replace with -x^2

e^-x^2 = 1 - x^2 + x^4 / 4! - x^6 / 3!

You can then do the approximation with integrating those