(20 pts) Usable value of the sine-integral function. The sine-integral function, si in t sin r is one of the many functions in engineering whose formulas cannot be simplified. i.e. there is no elementary formula for the anti-derivative of (sin t)/t. The values of Si(x), however are readily estimated by numeral integration. Although the notation does not show it explicitly, the function being integrated is sin f a. Prove that f(t) is continuous on R. The function ftt) has derivatives of all orders at every point of its domain. Its graph is smooth, and we can expect good results from Simpson's Rule. To approximate Si(x) Estimates(s) by using Simpson's Rule with N = 4 b (round your estimate to five decimal places (show all your work!) Usethefactthat1f4(,)|slfr, tofindan upper bound for thecrrorinyour answerto Find the smallest integer n so that|-5) d.
