Evaluate a integral by taylor series
correct your answer in 4 decimal places!!
the first step in my mind is find out the taylor series of e^x,sinx and lnx, and then multiply them all to obtain a new polynomial approximation so that we can integrate it without difficulties.
but the questions are....
1. although i can find the taylor series of e^x,sinx and lnx easily, how can we ensure the accuracy (4 deci. places)?
3assume that i can solve the above 2 problem, will the accuracy change AFTER the integration? and how?
i think it is difficult for me, plz give me some hints or reference to tackle this problem.
you can substitute 1/2 and 1 to check the accuracy.