Trapezoidal Approximation Help

[opus]

Homework Statement

Approximate each integral using the trapezoidal rule using the given number for $n$.
$\int_1^2 \frac{1}{x}dx$ where $n=4$

Homework Equations

Trapezoidal Approximation "Rule":

Let $[a,b]$ be divided into $n$ subintervals, each of length $Δx$, with endpoints at $P={x_0,x_1,x_2,...x_n}$
Set $T_n=\frac{1}{2}Δx\left[f(x_0)+2f(x_1)+2f(x_2)+...+2f(x_{n-1})+f(x_n)\right]$
Then,
$\lim_{n \rightarrow +\infty}T_n = \int_a^b f(x)dx$

The Attempt at a Solution

(i) $n=4$ and my intervals lengths are $Δx=\frac{b-a}{n}=\frac{1}{4}$

(ii) $\int_1^2 \frac{1}{x}dx ≈ \frac{1}{2}⋅\frac{1}{4}\left[f(1)+2f(1/4)+2f(1/2)+2f(3/4)+f(2)\right]$

$f(1)=1$
$2f(1/4)=8$
$2f(1/2)=4$
$2f(3/4)=\frac{8}{3}$
$f(2)=\frac{1}{2}$

Plugging the values into $T_n$, I get $\int_1^2 \frac{1}{x}dx ≈ 2.02$
The correct solution is 0.697, and I can't for the life of me see where I went wrong.

Could I get an extra pair of eyes on this?

 

[Orodruin]

Why are you evaluating at 1/4, 1/2, and 3/4? They are not in your interval.

 

[opus]

I am a fool. Should be 1 1/4 not 1/4 etc. Jeez. Thank you!