Let f(x) = e
-x2 and let I =
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dx. Given that
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≤ 12 for 0 ≤ x ≤ 1, what is the smallest value of n for which the Simpson's Rule approximation I ≈ S
2n will have error less than 0.0005 in absolute value? Hence, what is the value of I rounded to 3 decimal places?
◦ n = 4, I ≈ S
8 ≈ 0.747
◦ n = 2, I ≈ S
4 ≈ 0.747
◦ n = 3, I ≈ S
6 ≈ 0.747
◦ n = 1, I ≈ S
2 ≈ 0.747
◦ n = 3, I ≈ S
8 ≈ 0.747