Question

How to do Errors in Trapezoidal Rule and Simpson's Rule?
See below for question.

Answer 1

\[\int\limits_{0}^{2}x^3dx\]
n=4

Answer 2

I know the formula is
\[E \le \frac{ (b-a)^2 }{ 12n^2 } (\max \left| f"x \right|), a \le x \le b\]
and I got
1/4
but the answer is 1/2
am i doing something wrong?

Answer 3

@Hero @zepdrix

Answer 4

someone please help????

Answer 5

ok, i got the answer, but i don't get what they did in the last step.
(maximum when x=2?)