Question

Calculus Help!!
Evaluate the indefinite integral as an infinite series
∫sinx /3x dx.
Find the first five non-zero terms of series representation centered at x=0.
f(x)=
What is the radius of convergence?
i think it is infinity!!
Note: Remember to include an arbitrary constant "C".

Answer 1

i put f(x)=x/3-x^3/54+x^5/1800-x^7/105840+x^9/9797760+...
and R=infinity and it is nor correct!!
What did i do wrong?

Answer 2

Perhaps you might like to use this:
http://algo.inria.fr/esf/function/SI/SI.pdf

Answer 3

that's what i did.and my question has to divided it by 3x

Answer 4

Divide by 3 after we found that series... But what's the supposed correct answer?

Answer 5

i am not sure!!

Answer 6

find the series (or rather write the series) for sine
divide by 3x term by term
integrate term by term
that should do it right?

Answer 7

sinx=x-x^3/3!+x^5/5!-x^7/7!+x^9/9!
sinx/3x=1/3-x^2/18+x^4/360-x^6/15120+x^8/1088640
∫sinx /3x dx=x/3-x^3/54+x^5/1800-x^7/105840+x^9/9797760

Answer 8

R=infinity

Answer 9

I will do it for you when I come back from my morning walk.

Answer 10

okay,thanks!!

Answer 11

i put this too but it show incorrect!!so i don't know what i miss!!

Answer 12

2n+1 are the odds; not n+1

Answer 13

\[sin(x)=\sum^{inf}_{n=0}\frac{(-1)^nx^{2n+1}}{(2n+1)!}\]
\[\frac{sin(x)}{3x}=\sum^{inf}_{n=0}\frac{(-1)^nx^{2n}}{3(2n+1)!}\]

Answer 14

but isn't it the first five terms are the same?
where you divide sinx by 3x
sinx=x-x^3/3!+x^5/5!-x^7/7!+x^9/9!
sinx/3x=1/3-x^2/18+x^4/360-x^6/15120+x^8/1088640
∫sinx /3x dx=x/3-x^3/54+x^5/1800-x^7/105840+x^9/9797760

Answer 15

\[\int \frac{(-1)^nx^{2n}}{3(2n+1)!}\to\ \frac{(-1)^n}{3(2n+1)!}\int x^{2n}=\frac{(-1)^n x^{2n+1}}{3(2n+1)(2n+1)!}\]

Answer 16

\[\frac{x}{3*1!}-\frac{x^3}{9*3!}+\frac{x^5}{15*5!}-\frac{x^7}{21*7!}+\frac{x^9}{27*9!}\]

Answer 17

that's what i put too!!
and R=infinity!!but it is incorrect!!

Answer 18

im not sure what R equals yet :) but ive got to go fer now

Answer 19

okay.it also Note: Remember to include an arbitrary constant "C".

Answer 20

but when it doesn't let me to put C

Answer 21

if your wroking with a mathing program; make sure your answering acording to its "format"

Answer 22

i am sure it is the format but just doesn't say it is correct:(

Answer 23

i got it now.i have to put C for the first term!!

Answer 24

Thanks everyone!!