Thread: Using series to evaluate integrals

Use series to approximate the integral from 0 to 1 of...

((e^x)-1)/x dx

Write out 4 terms but do not add them.

Any help would be GREATLY appreciated....

Originally Posted by TwentyBucks

Use series to approximate the integral from 0 to 1 of...

((e^x)-1)/x dx

Write out 4 terms but do not add them.

Any help would be GREATLY appreciated....

The integral you gave is not a good integral.
Because the function is not defined on [0,1]
That means we need to appeal to improper integrals.

You can write out e^x as 4 terms:

e^x = 1+x+x^2/2 + x^3/6

Then,

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

Thus,

(e^x-1)/x = 1 + x/2 + x^2 / 6

Now this is a polynomial you can integrate this easily.

That's all I had to do? I thought I needed to find a series to represent the whole function...

Thanks so much for the help.

Originally Posted by TwentyBucks

That's all I had to do? I thought I needed to find a series to represent the whole function...

Thanks so much for the help.

the question said to do only the first 4 terms, so there was no need to find the series to represent the "whole" function