Trapezoidal Rule Homework: Equations and Solutions

[iRaid]

Homework Statement

Part b.

Homework Equations

The Attempt at a Solution

Well I thought the trapezoidal rule was:
$$\int_a^b f(x)dx = \frac{b-a}{2n}[f(1)+2f(2)+2f(3)+...+f(n)]$$

But when I did that I got the wrong answer and the work shows a completely different formula that I didn't know:

The part I'm confused about is the (2((66+60)/2)+...)

 

[jedishrfu]

(66+60)/2 is the avg height and 2 is thw dith of the segment so then 2*(66+60)/2 = area of that segment. add them up to get the approx area under the curve.

 

[iRaid]

Why is there an 2, then 3, then 4, then1 infront of each of the areas of the segments :|

 

[Mark44]

Why is there an 2, then 3, then 4, then1 infront of each of the areas of the segments :|

The first subinterval is of width 2 (sec); the 2nd's width is 3 sec; the 3rd's width is 4 sec; the last subinterval's width is 1.