<p>How exactly do you do trapezoidal rule when they give you a chart of all the x and f(x) values? Do you just do 1/2(f(a)+2f(b)+2f(c)+f(d)) (assuming there are only 4 numbers). If so, what is the reasoning behind that? Without a chart I would go (1/2)((b-a)/n) (f(a)+2f(a+ delta x)+ 2f(a+ 2 delta x)...etc.)</p>
<p>Am I right? Help! And does anyone have a link to year 2000+ collegeboard AB Multiple Choice Tests? Or is doing well on Barron's sufficient?</p>
<p>Would be much easier if you give me the problem…</p>
<p>depends if the intervals are even or not.</p>
<p>Sorry:</p>
<p>Time- 0 | 1 | 2 | 3|
Spd- 30|22|12| 0| </p>
<p>Estimate the distance the object travels using the trapezoid method.
I know that it’s 1/2(30+44+24+0), but why?</p>
<p>In geometry, the area of a trapezoid is 1/2 times the height times the quantity of both bases. On that graph, the speed is going to serve as the “base” because your estimations are going to be sideways trapezoids. Every time interval is 1 second, so the “height” here (distance between the bases) is going to be 1. You get .5*[(30 + 22) + (22 + 12) + (12 + 0)].</p>
<p>TRAM is an estimation of the integral.
To find the area of a trapezoid, it’s base/2 * (height1 + height2)
Since the base is 1 for each trapezoid, it is
1/2 * ((height at 0 + height at 1) + (height at 1 + height at 2) + (height at 2 + height at 3)) = 1/2 * (height at 0 + (2 * height at 1) + (2 * height at 2) + height at 3) = 1/2 * (30 + 44 + 24 + 0) = 49.</p>
<p>That helped a LOT! Thanks so much! So if the interval is an integer other than 1, say 2, would the two be on the outside of the parentheses, and be distributed along with the 1/2?</p>
<p>^ Yes. You know what to do if the intervals aren’t even though, right? On most problems I’ve seen, the intervals aren’t even…</p>
<p>I do, but is there like just 1 big, easy way to remember all of this besides just thinking through how to make a trapezoid? T_T</p>