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**problem on trapezoidal rule ????**

## Homework Statement

The error of the trapezoidal rule is equal to [(b-a)^(3)/n^2]*f''(e)

so when we want to find the integral to a given accuracy what we do is we find the maximum f'' value at that interval and subb that in the above equation .So that is the maximum error .Then if we want to have a accuracy of 5 decimal places then we find n (no of terms ) S.T

R<5*10^(-6)

i think i said it rightly >my question is in a problem in my book

Integrate (e^(-x^(2)/2) from 0 to 2 (function in standard normal distribution )

then after calculating we can get that max f'' in that interval is 0.4462 which we get when x=square root(3)

in my book they have said that

f''(x)<=1 in that interval instead of saying f''(x)<=0.4462

WHY IS THAT ???That change makes a huge difference in the required no of terms ....can someone explain why ?

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