Approximating Integrals using the Midpoint and Trapezoidal Rules
Channel: Andrew Misseldine
Date: 2020-07-02

In this video, we demonstrate how to approximate an integral using the Midpoint and Trapezoidal Rules. We also compute the error of these approximations. 

This is lecture 17 (part 2/4) of the lecture series offered by Dr. Andrew Misseldine for the course Math 1220 - Calculus II at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at: https://drive.google.com/file/d/1crXF4U2SsW0u53jr3L3OCpirKN35TLS_/view

This lecture is based upon Section 7.7 of Calculus by James Stewart. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.

The following links provide online Reimann Sum calculators and may be helpful:
https://www.desmos.com/calculator/6nmoluhram 

http://mathworld.wolfram.com/RiemannSum.html 
When using this app for the Riemann sum calculations, special named function are formatted in the following way: Cos[x]. The first letter should be capitalized and the x is surrounded by square brackets [...]. Also, use "Log[x]" for the natural logarithm. This calculator also has no Trapezoidal Rule, but this can be calculated by averaging together the Left and Right Rules.

http://www.emathhelp.net/calculators/calculus-2/riemann-sum-calculator/
I recommend taking off "Show Steps" after you get a feel for the types of calculations. This is a nice calculator but the ads are very annoying. Beware!

http://www.wolframalpha.com/widgets/view.jsp?id=ec54361d4124893a36d4feb3f7d4b6b8 
This calculator also does not have a Trapezoidal Rule.