# DOUBT in numerical integration

• bhartish
In summary, you may be able to numerically integrate the error function and exponential, but it's not guaranteed and you should be careful to check for errors.

#### bhartish

I have doubt in MATLAB

How to integrate

exp(x)*erfc(x) ? in MATLAB

The warning msg it is displaying is :

EXPLICIT integral could not be found

Are you trying to do numerical or symbolic integration? Maybe that's a function which has no analytic integral? If numerical, what are the limits?

I have an expression involving seven parameters. I need to first integrate the entire expression from 0 to t and then get the values by substitution method. Matlab is not supporting symbolic integration. hence I am planning to Numerical .

Oops I didn't see the title of you message. In that case there must be something wrong with your Matlab code since it should be able to integrate anything it can evaluate. Could you paste the code, including the limits of the integration?

Seems like a function that can easily be numerically integrated over any range of x.

Does it actually produce a solution, but you don't trust it because of the warning message?

e^(a+bt) erfc(-c+rt)exp((t-q)/l)

within the limits o to t

If you're using undefined a, b, c, r, q, and l, that's not numerical integration (especially if you're also attempting to integrate to an undefined 't').

I have all the values of a, b, c, r, q, l and t. Then how to go about it ?

Write a small script to do so. For instance, the following uses the trapezoid rule to find the integral between 0 and pi of the sine function.

Code:
	t=0:pi/100:pi;	% t values
y=sin(1*t);		% calculation of function at all t
A = trapz(y,t);	% implements trapezoid rule

Why did I explicitly use 1*t? While I could have just used t, it's to illustrate that there is no implicit multiplication in MATLAB (i.e. rt refers to the value / vector / matrix rt, while r*t refers to the product of r and t). I'd suggest writing up a small function (just as I've done above) in Notepad / Text Editor / EMacs / Vi, and then paste it here between the [code ][/ code] tags (no spaces in the tags).

I will get back to you sir.

I will clear one doubt. rt is r*t only. rt is definitely not a single variable.

I have one doubt can't we take some fictitous value and start integration of error function and exponential ?

bhartish said:
I will clear one doubt. rt is r*t only. rt is definitely not a single variable.

I have one doubt can't we take some fictitous value and start integration of error function and exponential ?

It's your work--you can put in whatever you want!

## 1. What is numerical integration and why is it important in scientific research?

Numerical integration is a method used to approximate the value of a definite integral, which is the area under a curve. It is important in scientific research because many real-world problems involve complex functions that cannot be solved analytically, and numerical integration provides a way to calculate these values with a high degree of accuracy.

## 2. What is the difference between numerical integration and analytical integration?

Analytical integration involves finding the exact solution to a definite integral using mathematical formulas and techniques, while numerical integration uses algorithms and numerical methods to approximate the solution. Analytical integration is only possible for a limited set of functions, while numerical integration can be applied to a wider range of functions.

## 3. How does the choice of numerical integration method affect the accuracy of the results?

The accuracy of the results depends on the complexity of the function being integrated and the choice of numerical integration method. Some methods, such as the trapezoidal rule, are less accurate but easier to implement, while others, like Simpson's rule, are more accurate but require more computational resources. It is important to choose a method that is suitable for the specific problem at hand.

## 4. Can numerical integration be used for any type of function?

Numerical integration can be used for any function that can be evaluated at a given point. However, the accuracy of the results may vary depending on the type and complexity of the function. Some functions, such as those with sharp corners or discontinuities, may require special methods or adaptations to be integrated accurately.

## 5. How do you know if the numerical integration results are reliable?

The reliability of the results can be assessed by comparing them to the exact or known solution, when available. Additionally, the convergence of the results can be checked by increasing the number of intervals or iterations in the numerical integration method. If the results remain stable and approach the known solution, then they can be considered reliable.