Question

Explain this?
See below.

Answer 1

\[\int\limits_{0}^{1} \frac{ 1 }{ x+1 }\]
when n=4
trapezoidal rule/simpson's rule error

Answer 2

oops i forgot a dx

Answer 3

\[E _{trapezoidal} =\frac{ (b-a)^3 }{ 12n^2 }(\max \left| f"(x) \right|) \]
how would you find f"(x)? and how did they get 2?
f"(x) = -2(x+1)^-3

Answer 4

wait, i see what i did wrong...

Answer 5

write f as\[f(x)=(x+1)^{-1} => f'(x)=-1(x+1)^{-2} => f''(x)=-1*-2(x+1)^{-3}\]So\[f''(x)=2(x+1)^{-3}=\frac{ 2 }{ (x+1)^3 }\]

Answer 6

yeah i saw what i did wrong. i forgot a negative >:(

Answer 7

Cheer up, you've found out yourself what went wrong!