Items tagged with definite_integral

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Dear all,

I would like to evaluate a double integral numerically. The integrand is a complicated function of the variables beta and s, with complex values. The computation lasts for decades without obtaining a result.

I was wondering whether there exists subroutines / methods / tricks that could be helpful to accelerate the integration process. I have attached a Maple script of the double integral of interest. Rough precision would be fine (4 or 5 digits).

Any help would be highly appreciated.

Thanks

Federiko

Question.mw

when i use the command evalf(Int(f(y),y=-b..b)), i expect that the output of this command to be an integer. but the output is to form of below:

i think that the problem is because of the form of the function f(y) that is the form of below:

f(y) = a*10^354*(b*10^-356*g(sin(y) , cos(y) and exp(y)))

but i dont know how i solve this problem:(

please help me. thank you

I can not find a solution to the integral of the function below the maple, can anyone help me?

 

restart;
with(Student[MultivariateCalculus]);
with(Student[Calculus1]);

assume(-1 < rho and rho < 1, alpha1 > 0, beta1 > 0, alpha2 > 0, beta2 > 0, t1 > 0, t2 > 0)

f := proc (t1, t2, alpha1, beta1, alpha2, beta2, rho) options operator, arrow; (1/4)*(sqrt(beta1/t1)+(beta1/t1)^(3/2))*(sqrt(beta2/t2)+(beta2/t2)^(3/2))*exp(-((sqrt(t1/beta1)-sqrt(beta1/t1))^2/alpha1^2+(sqrt(t2/beta2)-sqrt(beta2/t2))^2/alpha2^2-2*rho*(sqrt(t1/beta1)-sqrt(beta1/t1))*(sqrt(t2/beta2)-sqrt(beta2/t2))/(alpha1*alpha2))/(2-2*rho^2))/(alpha1*beta1*alpha2*beta2*Pi*sqrt(1-rho^2)) end proc

int(int(f(t1, t2, alpha1, beta1, alpha2, beta2, rho), t2 = 1 .. infinity), t1 = 0.1e-2 .. y)

 

Quite accidentally I discovered incorrect calculation of the simple definite integral:

int(1/(x^4+4), x=0..1);  

evalf(%);

                            1/8*ln(2)-1/16*ln(5)+1/32*Pi+1/8*arctan(1/3)   # This is incorrect result

                                                   0.1244471178

Is this a known bug?

 

If  first we calculate corresponding indefinite integral, and then by the formula of Newton - Leibniz, that everything is correct:

F:=int(1/(x^4+4), x):

eval(F, x=1)-eval(F, x=0);

evalf(%);

                                             1/16*ln(5)+1/8*arctan(2)

                                                     0.2389834593

 

 

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