Numerical+Integration





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Definition :
The process of finding the area under a particular curve by dividing the area into many tiny rectangles, adding up the heights of individual rectangles, and then multiplying the sum by their common width.

Video :
media type="youtube" key="Gi8_a7NlKAQ" height="350" width="425"

Steps :
1. Sketch the region 2. Establish whether f(x) is increasing/decreasing - If increasing: Left rectangular approximation (LRAM) will be the LOWER sum (less than actual area) and Right rectangular approximation (RRAM) will be the UPPER sum (greater than actual area) - If decreasing: LRAM will be UPPER sum and RRAM will be LOWER sum 3. Determine the number of rectangles or trapezoids (n) 4. Find **delta** x - Width of each rectangle - Height of each trapezoid 5. Use formulas to solve for the estimated Area

Examples :
 **1.)**

 //Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr//

**2.)**

 //Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr//

**3.)**



 //Graph made from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/riemann.html#instr//

4.)





**<span style="color: rgb(244, 230, 42);"> 5.) **

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">//http://www.calculus-help.com/probs1998/problem15.html//

<span style="color: rgb(128, 0, 128); font-size: 130%;">Practice Links :
[|Practice right, left, and midpoint approximations] [|Left, right and trapezoidal riemann sums] [| Upper and lower riemann sums]<span class="wiki_link_ext">