Monte Carlo Integration for ∫ xdx/(2+3x)^2 with Bounds of 0 and 1

In summary, the conversation discusses how to perform a Monte Carlo integration using 10 trials and at least 100 data pairs per trial. The method involves generating random x and y values between 0 and 1, with the condition that y is less than or equal to x/(2+3x)^2. The conversation also mentions using a spreadsheet or programming language for larger samples. Ultimately, the goal is to approximate the integral and find the ratio of successful trials to total number of trials.
  • #1
chimath35
110
0

Homework Statement


Perform a Monte Carlo integration of:

∫ xdx/(2+3x)^2 with the bounds of 0 and 1 on the integral

You should use 10 trials of at least 100 data pairs per trial and average the result

I guess I am supposed to generate a x and y random number between 0 and 100 and if the output of
y=x/(2+3x)^2 is equal to the y ran I count it

I really only know and have been shown how to use libre calc not sure how to do this

Homework Equations

The Attempt at a Solution

 
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  • #2
chimath35 said:
I guess I am supposed to generate a x and y random number between 0 and 100
What is between 0 and 100?
chimath35 said:
and if the output of
y=x/(2+3x)^2 is equal to the y ran I count it
It won't be equal exactly, there is a different condition (hint: you are approximating an integral).

Every spreadsheet can do that, programming languages would be better for larger samples but for just 100 data pairs it does not matter.
 
  • #3
okay so I pick an x value between 0 and 1 (random) and what do I pick the y value between?
 
  • #4
I have the actual value of the integral and I know it is a ratio of y≤x/(2+3x)^2 count as success/ of total # of trials for each x value
 
  • #5
Never mind, I understand the process now and have solved the problem. Thank you for the input.
 

1. What is Monte Carlo integration?

Monte Carlo integration is a numerical method used to approximate the value of a definite integral. It involves randomly selecting points within a given interval and using these points to estimate the area under a curve.

2. How does Monte Carlo integration work?

Monte Carlo integration uses the concept of probability to calculate the value of an integral. By randomly selecting points within the bounds of the integral, the method creates a sample of points that can be used to approximate the area under the curve. The more points that are used, the more accurate the approximation will be.

3. What are the advantages of using Monte Carlo integration?

One advantage of Monte Carlo integration is that it can be used to approximate integrals that are difficult to solve analytically. It also has the ability to handle high-dimensional integrals that may be challenging for other numerical methods.

4. What are the limitations of Monte Carlo integration?

Monte Carlo integration can be computationally expensive, especially for high-dimensional integrals. It also relies on the assumption that the function being integrated is continuous, which may not always be the case.

5. How do I implement Monte Carlo integration in my research?

To use Monte Carlo integration, you will need to write a computer program that generates random numbers and uses them to estimate the integral. There are also many software packages and libraries available that have built-in functions for Monte Carlo integration.

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