Need help with Taylor expansion of an integral:
integral from o to 1 of Sin(t)/t
I am having trouble setting this Taylor series up...for example, will the a=1? I know I need to use (x-a)^n/n! to set up the polynomials, but I'm not sure what a would be.

Question

Need help with Taylor expansion of an integral:
integral from o to 1 of Sin(t)/t
I am having trouble setting this Taylor series up...for example, will the a=1? I know I need to use (x-a)^n/n! to set up the polynomials, but I'm not sure what a would be.

anonymous · Answer

$$\int\limits_{0}^{1}\sin t/t $$

turingtest · Answer

nope, I don't think I know what we're talking about here...

turingtest · Answer

oh but apparently I just went up a level for typing that remark lol

anonymous · Answer

Oh also, when solving for the coefficients, should I plug in zero or 1?

hero · Answer

Welcome to level 99

turingtest · Answer

haha

anonymous · Answer

@mdntjem 
u just need to write taylor expansion of  $\sin t$ 

for $-\infty<t<\infty$
$$\sin t=\sum_{n=0}^{\infty} (-1)^n\ \frac{t^{2n+1}}{(2n+1)!}$$

turingtest · Answer

why does it talk about the integral then?

turingtest · Answer

I don't see the relation...

anonymous · Answer

so when I find the dervatives, I just use sinx not sinx/x?

anonymous · Answer

well... i think she wants to represent the integral $$\int \frac{\sin t}{t}dt$$ in the form of a series

anonymous · Answer

Yep, that's what the integral is supposed to look like, but it's missing the limits.

turingtest · Answer

so you still want to integrate the series term by term or what?

turingtest · Answer

because I suppose you could do that, right?

anonymous · Answer

@mdntjem  divide by t that expression mukushla mentioned above.

turingtest · Answer

...and then integrate it, yes?

anonymous · Answer

yes

turingtest · Answer

ok that makes some sense
but how do you evaluate it as a definite integral?

anonymous · Answer

answer will be a series again...

anonymous · Answer

Oh I did not know you could do that, thanks! Yea, I just need to find the first 3 NON-zero terms of the series and the add em up

anonymous · Answer

its easy . it depends on  the margin of error. she can integrate a few terms. (it will be series but she can add the terms to get value ). there will be some error associated.

anonymous · Answer

but I am still confused would my a=1 when evaluating the polynomials? And would this be centered around zero since I was not give a value?

anonymous · Answer

I think the question should have been to find the taylor approximation about a=0  (maclaurin series).otherwise it would not be possible to approximate the given integral .
Can you check your Question in the book again.?

anonymous · Answer

i think she has problem with choosing $a$ for writing taylor expansion...she can use both  $a=0$ and  $a=1$ (or any other neighborhood) for evaluating the integral.... better to use $a=0$ brcause obtaining the coefficients will be very easy about $a=0$...

anonymous · Answer

Okay, your guys are right, it does not make sense for a=1 I just wrote it all out

anonymous · Answer

Because I need to plug 1 in for x in order to evaluate the series

anonymous · Answer

Thank you all for your help!