Integral (with respect to d(z/σ))

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The discussion revolves around evaluating a specific integral related to a probability distribution function, with defined limits d and h, and standard deviation σ1. The user is seeking guidance on how to numerically evaluate the integral with respect to d(z/σ1). A suggestion is made to use the substitution u = z/σ1, which would require adjusting the limits accordingly. The conversation also touches on the implications of changing variables in integrals, specifically how to handle the limits after substitution. Clarification on these mathematical concepts is requested to aid in the user's research paper review.
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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.
 

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