If statement for Monte Carlo integration

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SUMMARY

This discussion focuses on implementing an if statement in Fortran for Monte Carlo integration to calculate the integral of sin^4(x) over the interval from 0 to π/2. The user seeks guidance on determining whether randomly generated points fall within the area under the curve defined by the function. The key insight provided is that the if statement should check if the points are "under the curve" to accurately estimate the integral.

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  • Fortran programming language
  • Monte Carlo integration techniques
  • Understanding of the integral of sin^4(x)
  • Knowledge of bounding rectangles in numerical methods
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  • Research how to implement random point generation in Fortran
  • Study the mathematical principles behind Monte Carlo integration
  • Learn how to evaluate functions to determine if points are under a curve
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Mathematicians, Fortran developers, and anyone interested in numerical integration methods using Monte Carlo techniques.

mayankbhargava101
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Hello,

I am writing a program on Fortran to calculate the integral of sin^4(x) between x = 0 and x = π/2.

I believe I know how to write the correct code, but I am unsure what the if statement should be for whether or not a point is inside the desired area.

Any thoughts?

Thanks.
 
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mayankbhargava101 said:
Hello,

I am writing a program on Fortran to calculate the integral of sin^4(x) between x = 0 and x = π/2.

I believe I know how to write the correct code, but I am unsure what the if statement should be for whether or not a point is inside the desired area.

Any thoughts?

Thanks.
I assume that you are generating random points within a bounding rectangle. Since you are calculating an integral, you will want the area under the curve. The operative phrase would be "under the curve".
 

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