# Integral (with respect to d(z/σ))

• MechEng2010
In summary, the conversation is about an individual who has uploaded an integral with defined limits and is seeking help on how to evaluate it numerically. Another person suggests substituting u=z/σ1 and explains how it would affect the limits. The first individual asks for further clarification on the substitution and its effect on the limits. The second individual then asks the first to consider the values of dz/du and d(z/s)/du.
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.

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• Inetgral.GIF
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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.

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.

## 1. What is an integral with respect to d(z/σ)?

An integral with respect to d(z/σ) is a type of integration where the variable of integration is a function of z and σ. This type of integral is commonly used in statistics and probability to calculate probabilities and expected values.

## 2. How is an integral with respect to d(z/σ) different from a regular integral?

An integral with respect to d(z/σ) is different from a regular integral because the variable of integration is a function, rather than a single variable. This means that the limits of integration and the integrand may also involve z and σ.

## 3. What is the purpose of using an integral with respect to d(z/σ)?

The purpose of using an integral with respect to d(z/σ) is to integrate functions that involve both z and σ. This type of integral is particularly useful in statistics and probability, where z and σ are often used to represent random variables.

## 4. What are some applications of integrals with respect to d(z/σ)?

Integrals with respect to d(z/σ) have many applications in statistics and probability. They are commonly used to calculate probabilities, expected values, and moments of random variables. They are also used in the derivation of statistical distributions and in statistical inference.

## 5. How do I solve an integral with respect to d(z/σ)?

Solving an integral with respect to d(z/σ) follows the same principles as solving a regular integral. You must first determine the limits of integration and the integrand, and then use techniques such as substitution, integration by parts, or partial fractions to evaluate the integral. It is important to keep in mind that the final result will be a function of z and σ.

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