Please help - Power Series Question?

Question

Hey can anyone help me out with this question please??

Use five terms in a power series to estimate:
Integral 0 to 0.2 of (arctan(t^(2)))/(t) dt
(the arctan is in the top of the fraction not preceding it)

Please help!!

Answer 1

Arctan z= = z-z^3/3+z^5/5-z^7/7
z=t^2
Arctan t^2 /t = t-t^5/3+t^9/5-t^13/7
The integral from o to0.2 is

(0.2)^2/2 -(0.2)^6/18+(0.2)^10)/50-(0.2)^14/98
You can do the numbers

Answer 2

Answer is in my link below , at the bottom

http://answers.yahoo.com/question/index;_ylt=AvvWBZA1Fx5K8e3xJ.9Hka7ty6IX;_ylv=3?qid=20071205185017AAb9YP8&show=7#profile-info-IDabPOsQaa