Riemann Sum Question: Is my Answer Correct?

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SUMMARY

The discussion centers on the accuracy of a Riemann sum approximation for the integral of the function sec(x/3). The user questions the use of 32 as the denominator in the provided solution, asserting that their calculations yield a denominator of 12 based on the formula Δx = π/6. The user clarifies that they intended to use π/12 for the first midpoint and acknowledges a mistake in omitting function notation around their fractions. The conversation highlights the importance of correctly applying Riemann sum principles in integral approximations.

PREREQUISITES
  • Understanding of Riemann sums and their application in calculus.
  • Familiarity with integral calculus concepts, specifically midpoint approximations.
  • Knowledge of trigonometric functions, particularly secant functions.
  • Ability to manipulate fractions and perform basic algebraic operations.
NEXT STEPS
  • Study the derivation of Riemann sums and their applications in calculus.
  • Learn how to calculate Δx for different types of Riemann sums.
  • Explore the properties and applications of the secant function in calculus.
  • Practice solving integral problems using various approximation methods, including trapezoidal and Simpson's rule.
USEFUL FOR

Students studying calculus, educators teaching integral approximation methods, and anyone looking to improve their understanding of Riemann sums and their applications in solving integrals.

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Hello, just going through some Riemann sum problems before I hit integrals and I am like 99% sure that this answer from my text is wrong but I want to make sure. It's not really an important question so if you have better things to do, help the next guy :) But checking this over would be appreciated!

http://img178.imageshack.us/img178/875/incorrectyp5.jpg

I am trying to find an approximation of the integral using a Riemann sum.

Here is the question.

http://img216.imageshack.us/img216/2113/incorrect2jj8.jpg

Why are they using 32 as the denominators for their endpoints? I have the same numerators but my denominator is 12 since \Delta x=\frac{\pi}{6}. And for my first midpoint I would use half that.. \frac{\pi}{12}, and then add delta x again n times, right?
 
Last edited by a moderator:
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It's sec(x/3).
 
Sigh, how dumb of me... thanks, arg!

If I had f()'s around my fractions I would have been fine, forgot about that. :( Thanks though, and sorry.
 
Last edited:

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