Approximating Integrate Using Series Methods

[blue mango]

I need help solving the following (it is due tomorrow and it just got assigned yesterday ):

use series methods to obtain the approximate value of integral(from 0 to1) of (1-e^x)/x dx

What I have thought of so far is to use the Taylor series approx for e^x and carry that out to a few terms then solve for 1 and 0 and plug it into the original equation but I'm not sure that I'm headed in the right direction. I took a year off from school and now I'm having to relearn a bunch of things that were once simple but now seem quite challenging. Any help is appreciated. Thanks.

 

[hunt_mat]

Looks good to me. You should get an easy power series to integrate and then you just substitute in 1 and 0.

Mat

 

[blue mango]

I plugged in the Taylor series for e^x and took that out to 6 terms then integrated it from 0 to 1 and got 1.262...does that sound about right?

 

[Office_Shredder]

The integrand is negative so you should end up with a negative answer.

As an example just using two terms, e^x=1+x you would end up with

$$\int_0^1 \frac{1-(1+x)}{x}dx = \int_0^1 \frac{-x}{x}dx=-1$$

As you add more terms the integral should become more negative

 

[blue mango]

Thanks for pointing that out Office Shredder. There was a negative that I had forgotten to carry over. So I got -1.262 with 6 terms in the e^x Taylor series.