Question

help with simpson's rule error

Answer 1

Use the Error Bound to find the least possible value of N for which Error(SN)≤1×10^−9 in approximating \[\int\limits_{0}^{1}4e ^{x^2}dx\]
using the result that
\[Error(S _{N}) \le \frac{ K _{4}(b-a)^5 }{ 180N^4 }\]
where K4 is the least upper bound for all absolute values of the fourth derivatives of the function 4e^(x^2) on the interval [a,b].

Answer 2

i found the fourth derivative: = e^(x^2) (64x^4 + 192x^2 + 48) then i plugged in 1 for x and got 826.3577 then i plugged that into \[1\times10^{-9 }\le \frac{ K(b-a)^5 }{180N^4}\] \[1\times10^{-9}\le \frac{ 826.3577(1)^5 }{ 180N^4 }\] \[(180N^4)(1\times10^-9) \le 826.3577\] is this right so far or am i doing it wrong?

Answer 3

@myininaya

Answer 4

@satellite73

Answer 5

@ganeshie8