Confused on Solving a Series Computation: Help Needed!

[intervade]

Ok it says I am to computer using a series accurate to within 0.001.

I'm really not sure where to start. Do I integrate this first by parts? Or am I thinking about this too much? Could someone point me in the right direction please! Help would be much appreciated!

 

[Mark44]

Ok it says I am to computer using a series accurate to within 0.001.

I'm really not sure where to start. Do I integrate this first by parts? Or am I thinking about this too much? Could someone point me in the right direction please! Help would be much appreciated!

The key word is series here. Get the Maclaurin series for e^-x2, and then multiply it by x². Does that give you a place to start?

 

[intervade]

Ok let me just make sure I'm on the right track..

Is this correct to say?

sorry, my latex skills are bad.

 

[Mark44]

No, write the series in expanded form, not in closed form. Notice that because you have an alternating series, the error is less in absolute value than your first unused term.

Your LaTeX looks pretty good!

 

[intervade]

Hmm I'm not exactly sure what to do with this still. How do I integrate an expanded form of a series?

 

[Mark44]

Term by term. This series converges pretty quickly, so you shouldn't need a whole lot of terms.