1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Apostol: Archimedes' Method

  1. Jun 27, 2007 #1
    I've started with Apostol's first volume of calculus and I'm already having a problem with the first exercise in the book. Weak. It asks to use Archimedes' method to find the area under a parabola from 0<x<b for a parabola where y = a*b^2 + c. Using the summation of upper/lower rectangles of width b/n and height a(k*b/n)^2 +c. Now each rectangle has an area of a(k^2)(b/n)^3 + (bc)/n. k goes from 0 to n-1 for the lower rectangles and from 1 to n for the upper rectangles. My problem comes when summing up all of the rectangles using the arithmetic summation. I get the first portion correct, but end up with (bc)/n instead of bc as the second term in the area formula. Any way that I'm approaching this incorrectly or should approach this?
     
  2. jcsd
  3. Jun 27, 2007 #2

    StatusX

    User Avatar
    Homework Helper

    The sum bc/n+bc/n+...+bc/n (n times) is bc.
     
  4. Jun 27, 2007 #3
    Ah, right. Stupid of me to miss that result.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Apostol: Archimedes' Method
  1. Archimedes expiriment (Replies: 2)

  2. Apostol's Field Axioms (Replies: 6)

  3. Limits - Apostol book (Replies: 6)

Loading...