Riemann Sum Question: Is my Answer Correct?

In summary, the conversation is about a person going through Riemann sum problems and questioning the answer provided in the text. They are trying to find an approximation of an integral using a Riemann sum and have noticed that the denominators for the endpoints in the provided answer are different from what they would use. They also mention using f() around their fractions in order to get the correct answer.
  • #1
Checkfate
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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 [tex]\Delta x=\frac{\pi}{6}[/tex]. And for my first midpoint I would use half that.. [tex] \frac{\pi}{12}[/tex], and then add delta x again n times, right?
 
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  • #2
It's sec(x/3).
 
  • #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.
 
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1. What is a Riemann Sum?

A Riemann Sum is a method used in calculus to approximate the area under a curve by dividing the area into smaller rectangles and summing their areas.

2. How do you calculate a Riemann Sum?

To calculate a Riemann Sum, you need to divide the area under the curve into smaller rectangles and then sum their areas. The width of each rectangle is determined by the interval of the function and the height is determined by the function's value at a specific point within the interval.

3. What is the purpose of using a Riemann Sum?

The purpose of using a Riemann Sum is to approximate the area under a curve when it is not possible to find the exact area using traditional methods. It is also used to approximate other important values such as volume and average value of a function.

4. How do I know if my Riemann Sum is correct?

You can check the accuracy of your Riemann Sum by increasing the number of rectangles used in the calculation. As the number of rectangles increases, the approximation will become closer to the exact value. You can also use known methods to calculate the exact value and compare it to your Riemann Sum.

5. What are the limitations of Riemann Sums?

Riemann Sums can only provide an approximation of the exact value and may not be completely accurate. They also require a lot of calculations for a more precise approximation. Additionally, Riemann Sums are only applicable to continuous functions.

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