Numerical Integration by Matlab

Please mention about the tolerance of accuracy

[James Tursa]

What have you done so far? What specific problems are you having with your code? Are you directed to use a specific technique to come up with an approximation?

[Andy Tan]

I don't know how to start,can you provide me the answer?no,I am not directed to use a specific technique to come up with an approximation

[Walter Roberson]

integral()

[Andy Tan]

I can't just use the command,I want the code written by ourselves

[Walter Roberson]

You said that you are not directed to use a specific technique, so you can use integral(). Or vpaintegral().

[Andy Tan]

but if I use integral,I can't set the tolerance of accuracy?

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/integral.html#btbbkta-1-AbsTol

[Andy Tan]

I have tried but I want to set the tolerance of accuracy 10^-7 but the the results shown in the Matlab is 4decimal places,I don't think the AbsTol is effective?

[Walter Roberson]

Give the command

format long g

and then display the result again.

By default, MATLAB only displays 4 decimal places, but the values are stored internally to higher precision.

Answer 1

[James Tursa]

Hint: You might look here:

https://en.wikipedia.org/wiki/Normal_distribution

Knowing that the integral of the Normal density function from -infinity to +infinity is 1 exactly, maybe you can come up with a change of integration variable to get that equation in a form that matches your integral to get the exact answer directly. Starting with a standard Normal density function (mu=0, sigma=1), it is a pretty easy substitution from there to get what you have.