Riemann Sums on AP Calc

[lce]

<p>hey everyone, does anyone know how to do #18 on the BC part of the course description? [Page</a> Not Found](<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), page 35</p>

<p>also if anyone has a link for a tutorial for Riemann Sums in general, that would be greatly appreciated!</p>

[Islander4]

<p>[YouTube</a> - AP Calculus Riemann sums: Soup to Nuts](<a href=“http://www.youtube.com/watch?v=YHYT3HlL1uA]YouTube”>http://www.youtube.com/watch?v=YHYT3HlL1uA)</p>

[bobtheboy]

<p>Page not found…</p>

[ChemE14]

<p>

#18.</p>

<p>You want the Reimann Sum version of the integral of the cross-sectional area, which is</p>

<p>int(from 0 to 2) (1+3x)dx</p>

<p>this is equivalent to the Reimann Sum formula of</p>

<p>SUM(1 to n) f(x<em>i) * delta</em>x</p>

<p>f(x<em>i) = 1 + 3 (a + (b-a)*i / n), delta</em>x = (b-a) / n, a = 0 and b = 2 (because those are the bounds of integration), so</p>

<p>SUM(1 to n) [ 1 + 3 (0 + 2*i / n) ] * (2 - 0) / n</p>

<p>= SUM(1 to n) [1 + 6i/n] * (2/n)</p>

<p>You need to know the basic formula (above) and that x<em>i = a + delta</em>x * i, and also that delta_x = (b-a) / n

</p>

<p>Copy and pasted from my post a few minutes ago in the BC Study thread.</p>