<p>Does anyone get how to do this relating to Calculus AB for tomorrow?</p>
<p>For approximating the area under a curve?</p>
<p>You should be given an interval, which may or may not be partitioned. (It could be a graph, equation, or table. Most practice tests have had a table, at least.)</p>
<p>Next, you approximate the area like you’re finding the areas of trapezoids. Remember, the area of a trap is (1/2)(b1 + b2)h, where b1 = base one, and h = height (and so on). The function evaluated at a point is like the “base,” thereby making all your trapezoids sort of sideways. The height is the distance between the two points (how far you walk down the x-axis). Add together all your trapezoids to get an approximate area.</p>
<p>^ This.</p>
<p>There’s also a formula called the “Trapezoidal Rule” that a lot of the textbooks want to parrot. You don’t want to waste your time with that Rule (which basically takes all the 1/2h’s from each of the trapezoids and factors it out), because it only works in cases where the h values are uniform. The AP Test frequently tests the trapezoidal approximations by giving you uneven intervals for h.</p>
<p>ok so how would you do that then? so in other words the formula written in my textbook is useless? how would you do it if the intervals are uneven?</p>
<p>So take a question like 2005 AB#3b: <a href=“Supporting Students from Day One to Exam Day – AP Central | College Board”>Supporting Students from Day One to Exam Day – AP Central | College Board;
<p>The average temperature of the wire is 1/8 * integral(T(x), x, 0 , 8). integral(T(x), x, 0, 8) can be approximated using four trapezoids as follows:</p>
<p>Region, width * 1/2 * (sum of bases)
[0, 1]: 1 * 1/2 * (100 + 93) = 96.5
[1, 5]: 4 * 1/2 * (93 + 70) = 326
[5, 6]: 1 * 1/2 * (70 + 62) = 66
[6, 8]: 2 * 1/2 * (62 + 55) = 117</p>
<p>Sum of trapezoids: 605.5</p>
<p>1/8 * integral(T(x), x, 0 , 8) = 1/8 * 605.5 = 75.688 degrees Celsius.</p>
<p>You would multiply each trapezoid by its corresponding height, instead of factoring out one common height (you can do this for equal subintervals).</p>
<p>THANK u guys for ur help</p>