expand f(x)= xcosx up to x^3 differentiating many times my expansion is to find an approximate value for do I just plug in the limit values and evaluate as below?
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must I integrate first?
First of all, since this is clearly a calculus question, why have you posted in pre-calculus? Now you need to evaluate $\displaystyle \displaystyle \int{x - \frac{x^3}{2}\,dx}$ and then substitute the limits.
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