Items tagged with double-integral


I am trying to do the following double integral in tranches as listed here:

P := proc (x, y) options operator, arrow; (1/2)*exp(-(1/2)*(x^2+G*y^2-2*B*x*y)/(-B^2+G))/(Pi*sqrt(-B^2+G)) end proc

Since G and B are constant

((int(x = 0 .. infinity))*(int(y = -infinity .. 0))+(int(x = -infinity .. 0))*(int(y = 0 .. infinity)))*P(x, y)

But does notwork. How do I pass these coordinates to polar?


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.



How to find the double integral of sin(x^2)*cos(y^2) over the disk of radius R which is centered at the origin? 

Here is my try 

restart; evalf(VectorCalculus:-int(sin(x^2)*cos(y^2), [x, y] = Circle(`<,>`(0, 0), 1), inert), 15);



I'm solving a 2D grid with some finite-diference methods. The result is a surface, i.e f(x,y) = z. Where X and Y and points on a grid. 


I then need to integrate over this grid, i.e

int(f(x,y),[x=0..10, y=0..10]) 

I have tried interpolating the grid. I've used CurveFitting:-ArrayInterpolation() to interpolate points in this 2D space and then integrate over them. 

I'm using a 30x30 grid, but this interpolation scheme takes far too long. The function generated from the ArrayInterpolation creates an interpolation every time a point is evaluated, which I assume is why the integral is very computationally expensive. 

I would like to create a piecewise analytic function from the 2-D grid, perhaps using CurveFitting:-Spline(), however from my understanding this only works for 1D objects? 

Is there any better solution for integrating a 2D numeric grid?

Thanks in advance

How to find the integral

assuming k and n  integer?
It is known (McCrea W. H., Whipple F. J. W.Random paths in two and three dimensions, Proc. Roy. Soc. Edinburgh. 1940. V. 60. P. 281–298) that


The general case is reduced to the case k=n.
This is not a creature of pure reason: the one appears in electric circuits
(see M. Skopenkov, A. Paharev, A. Ustinov, Through resistor net, Mat. pros. Issue 18 (2014), 33-65, in Russian,
I found G(8,8) = 182144/(45045*Pi) in 657.797 s and G(9,9) = 3186538/(765765*Pi) in 4157.687 s on my comp by

restart; s := time():(1/2)*VectorCalculus:-int((1-cos(9*Pi*x)*cos(9*Pi*y))/(sin((1/2)*Pi*x)^2+sin((1/2)*Pi*y)^2), [x, y] = Rectangle(0 .. 1, 0 .. 1)); time()-s;
Mathematica 10.3.0 does G(9,9) in 250.391 s on my comp.


I would like integrate and plot the following double integral:


I enclosed

I've got the following double integral over a region A:

e^(1/x*y)/(y^2)*(x+1)^2 where A={(x,y):1/2<=x*y<=2,1<=x<=3}

to evaluate this:

I've tried :


since the largest lower bound and smallest upper bound for y based on 1/2<=xy<=2 are 1/2 and 2/3 respectively.

This statement however, only evaluates the inner integral; is my approach correct?

Hello everyone, I am having problem while trying to evaluate the double integral written in the file attached Please help me out.
Many thanks in advance.


I am trying to solve following expression

int(int((1-exp(-5.5/cos(x)))*sin(x), x = 0 .. arctan(300*cos(y)+sqrt(12.25-90000*sin(y)^2))), y = 0 .. Pi)

But I am not getting results.

Please help me!!!


hi.i am a problem for solve analytic double integration as blow,plese help me....Thanks alot

int(int((2*gamma*cos(psi)/(D-r*sin(theta)*sin(phi))-2*gamma*cos(psi)/(D+r*sin(theta)*sin(phi)))*r^2*cos(theta)*sin(phi), r = 0 .. L), phi = 0 .. Pi)



int(int((2*gamma*cos(psi)/(D-r*sin(theta)*sin(phi))-2*gamma*cos(psi)/(D+r*sin(theta)*sin(phi)))*r^2*cos(theta)*sin(phi), r = 0 .. L), phi = 0 .. Pi)



How to find the integral

1/(4*Pi)*int((cos(t)-sin(s)-cos(t)*sin(s))/(3+2*(cos(t) - sin(s) - cos(t)*sin(s)))^(3/2),[t=0..2*Pi,s=0..2*Pi])?

Its geometric interpretation suggests the answer is -1. Maple finds the inner integrals both over t and s, but Maple cannot directly find the iterated integrals.

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