Integral (with respect to d(z/σ))

[MechEng2010]

Hello all,

I have uploaded a .gif of the integral. The limits are just values, as I know what d,h, and σ₁ are. d and h are the lower and upper limits defined for the probability distribution function and σ₁ is the standard deviation.

I have not seen this type of integral before, I am not sure how I can evaluate this numerically as I need to do this with respect to d(z/σ))?

This is on a research paper I am currently reviewing, Can anyone help?

Thanks.

 

[Simon Bridge]

why not substitute $u=z/\sigma_1$ ?

 

[MechEng2010]

Would that help me to integrate this between the numerical limits of d/σ1 and h/σ1? Sorry still confused, could you explain further. Thanks.

 

[Simon Bridge]

If that's what you want to do.
Of course you'd have to substitute for the limits as well.

if you integrate from z=a to z=b but you make the the substitution in the integrand that u=f(z) then what happens to your limits?

But - if u = z/s, what is dz/du ? what is d(z/s)/du ? Put du = ... for each. Compare.

 

[CellCoree]

I can provide some insights on this type of integral. This is known as a Gaussian integral, also known as the normal integral. It is a special case of the more general integral known as the error function. This type of integral is commonly used in statistics and probability theory to calculate the probability density function for a normal distribution.

In order to evaluate this integral numerically, you will need to use a numerical integration method such as the trapezoidal rule or Simpson's rule. These methods approximate the value of the integral by dividing it into smaller sections and summing the areas of these sections. This can be done using software such as Matlab or Mathematica.

Additionally, it is important to note that the integral is with respect to d(z/σ), which means that the variable being integrated is d(z/σ) and not just d. This may affect the limits of integration and the overall calculation.

I hope this helps in your research and understanding of this integral. If you need further assistance, I suggest consulting with a statistician or mathematician who has expertise in this area. Good luck with your review.