1. Trapezoidal Rule

The exact value of $\int_{0}^{3 \pi} \sin x \ dx = 2$. How large must $n$ be for the Trapezoidal approximation $T_n$ to satisfy $|E_T| \leq (2-S_n)$?

2. Originally Posted by shilz222
The exact value of $\int_{0}^{3 \pi} \sin x \ dx = 2$. How large must $n$ be for the Trapezoidal approximation $T_n$ to satisfy $|E_T| \leq (2-S_n)$?
Do you have a formula for the bound on the error in using the trapezoidal rule?

Something like:

$
| \varepsilon | \le \frac{1}{2} h^2 (3 \pi) \{ \max_{x \in [0, 3\pi]} \sin(x) \}
$

in this case

RonL