Need help with the integral

Hello, how to write a code to find an excat value of this integral?

I really need help with this one! I wrote a code to approximate the value but i can't create a code to find the exact one

[Walter Roberson]

How do you want the exact value expressed? erf? hypergeometric function? Fresnel C function?

[Erika Plekaviciute]

The exact value must be a number equal to this: ?????? ~ 0.904524237900272

I created a code but it calculates only the approximate value, so I keep getting: 0.904524456832745

[Walter Roberson]

That isn't the exact value. The exact value is likely an irrational number when expressed in decimal; sqrt(pi) is part of the expression of it. Any finite truncation of it would be only an approximation.

What is your numeric approximation code? You only need 9 terms to get that particular numeric value.

[Torsten]

Because you write down a series representation of the integral, maybe your task is to add up until you get the required accuracy ?

[Walter Roberson]

You are just doing a summation of values at end points as if the value were constant for the entire interval. That is not going to be accurate. You should look at the trapizoid rule for greater accuracy. trapz()

[Torsten]

You are trying to approximate the integral, not summing up the series.

[James Tursa]

Erika, it is very poor online etiquette to delete your question after there have been comments and answers posted. This is a disservice to the Answers community.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Torsten]

format long
I = 0.0;
Iexact = 0.904524237900272;
eps = 1e-15;
n = 0;
while abs(I-Iexact) > eps
 I = I + (-1)^n/(factorial(2*n)*(4*n+1))
 n = n+1;
end
n-1
I