Question

am i doing this simpson's error problem correctly?

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
\[Error(S_N) ≤\frac{ K_{4}(b−a)^5 }{ 180N^4 } \]

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
1×10^−9 ≤ K(b−a)^5 / 180N^4

1×10−9 ≤ 826.3577(1)^5 / 180N^4

(180N^4)(1×10−9) ≤ 826.3577
is this right so far or am i doing it wrong?

Answer 3

when i solve for N i keep getting 260 but that's not the right answer.

Answer 4

:/

Answer 5

@darkigloo do you have any other guesses?

Answer 6

@ILovePuppiesLol @Directrix @Daniee_Bruhh @sleepyjess @HorseBabe96 @LovelyAnna

Answer 7

@Kainui