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### 032-Para Sings: "Don't Stop With Riemann"

posted Sep 29, 2013, 5:54 AM by Gregory Taylor
 PARA SINGS 12ax2 + bx + c  presents...."Don't Stop With Riemann"  (*aka "Don't Stop Believin'", Journey)--------Official video: Unable to locate (Copyright pull?)Live Band Performance: Vevo here Source Lyrics video: YouTube HereKaraoke version: YouTube HereGlee Lyrics version: YouTube HereKaraoke Glee Version: YouTube Here***Just approach from left,Estimate is low, I guess.We want the area underneath this curve.Just approach from right,Estimate is high, how trite.We want the area underneath this curve.(Instrumental)(Glee option call out: "Riemann!")A manner to approximate?A summation to contemplate!Every trial helps us to refineIt goes on and on and on and on...{Refrain:}Segments, added. Up or down along this curveTheir width we'll narrow, out of sight.Limit's useful, telling us to stop and observeGives us answers which are right!Working with unending sums,Series is what this becomes.Breaking vastness into discrete partsWe'll comprehend.Some see now, some years hence,Some may only grasp a sense!But the learning never ends,It goes on and on and on and on...{Refrain:}Segments, added. Up or down along this curveTheir width we'll narrow, out of sight.Limit's useful, telling us to stop and observeGives us answers which are right!(Instrumental)Don't stop with Riemann,Try some integration!Limits, useful, ohhhhhhh.Don't stop with Riemann,Try some!Limits, useful, ohhhhhhh!(repeating option)Graph pics from this site:http://www2.seminolestate.edu/lvosbury/CalculusI_Folder/RiemannSumDemo.htmExplore with your own sums here:http://www.mathopenref.com/calcriemann.html