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I am trying to approximate the following integral, using numerical integration in R:

,

where the function mu is defined by this formula:

To do this, I have implemented the Composite Simpson's rule as a function in R, which takes as parameters a function (integrand), the integration interval ([a,b]) and the number of subintervals desired (n).

I have tested my code on various different mathematical functions, and it seems to be working just fine. However, when I try to approximate the integral shown in the picture, the approximation becomes to large.

My method has been to first define the inner integral in terms of its Composite Simpson approximation as a function of t in R. Then, use the Composite Simpson's rule again, in order to calculate the outer integral by viewing the inner approximation as the function to be integrated.

When doing this, the inner approximation is correct when calculated by itself, as expected, but the approximation of the entire expression becomes too large, and I can't seem to figure out why.

I am comparing the approximations to those given by Maple; the inner expression calculated by itself, using t=20, should give 0.8157191, and the entire expression should be 12.837. R correctly calculates 0.8157191, but gives 32.9285 for the entire expression.

I have tried simplifying using numerous different mathematical functions, and making the functions independent of t in R, but all seems to result in the same error. So, to sum things up, my question is, why is only the outer integral being approximated wrongly?

I would be greatly appreciative of any hints or pointers - I have included my code illustrating the problem here:

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1- Here is my data

Note: this could be considered as a duplicate of Gcov is not generating *.gcda file, however :

1. This question has no answer
2. I don't think the OP has the same system than me, so I don't think it'll be ok for me to just go and edit his question. Moreover, the question is 5yo.
3. I produce here a "minimal" and reproducible example.

So, I was trying to reproduce an error that I had with gcov...and I run on another instead. Here are some files:

main.c:

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The code below is compiled with clang -Wall -O2 test.c LLVM-C.dll -o test

Output:

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This is the default interface for my program when it starts running. As you can see, it's just a small form control

enter image description here This is the default interface for my program when it starts running. As you can see, it's just a small form control