
maclaurin expansion
expand f(x)= xcosx
up to x^3
differentiating many times my expansion is
http://quicklatex.com/cache3/ql_06c3...37e773c_l3.png
to find an approximate value for
http://quicklatex.com/cache3/ql_277f...81c2edb_l3.png
do I just plug in the limit values and evaluate as below?
http://quicklatex.com/cache3/ql_6c07...1ea3a3f_l3.png


First of all, since this is clearly a calculus question, why have you posted in precalculus?
Now you need to evaluate $\displaystyle \displaystyle \int{x  \frac{x^3}{2}\,dx}$ and then substitute the limits.