Items tagged with integration

Feed

I recently encontered a very strange result.

Lets define the procedure:

Fg := proc(x0,y0)
if (x0>=0)and(x0<=3) and (y0<=x0+2) and (y0>=x0-1) and (y0>=0) and (y0 <=3) then
return y0*(3-y0)*x0*(3-x0)*(x0+2-y0)*(y0-x0+1);
else
return 0;
end if:
end proc:

The plot looks like needed:

plot3d('Fg'(x,y), x=0..3, y=0..3);

But integration returns weird result:

evalf(Int('Fg'(x,y), [x=0..1, y=0..2.1]));

7.888753239

evalf(Int('Fg'(x,y), [x=0..1, y=0..2.2]));

Error, (in evalf/int) when calling 'Fg'. Received: 'cannot determine if this expression is true or false: 0 <= x and x <= 3 and y <= x+2 and x-1 <= y and 0 <= y and y <= 3'

Fix_integrations.mw

Could you any one help me to fix this application and find the result for integrations?

 

Many thank,

Hi, I know the commands for when both curves/functions are y=....., but not when one of them is y=... and the other is a straight line going through the x-axis. I would like to be able to find the points of intersection in decimals, to plot them together such that I can see the points of intersection and finally I need to find he area enclosed between the two. Would appreciate your help.

Hello all,

So far I have been unable to find this question anywhere, but I apologize if it is a duplicate. I'm trying to evaluate the integral of sechq(x), where q is a positive integer. Mathematica is able to tell me the result (a hypergeometric function), but for some reason, Maple seems not to be able to compute this integral, it just gives me back the integral. A higher info-level on the 'int' function reveals a line that says 'Risch d.e. has no solution', but I'm not sure if that has anything to do with my problem. Any suggestions or tips on how to get an answer out of Maple would be greatly appreciated!

I want to calculate the following integral numerically with required precision.

First, the functions are defined:

G1:=-0.9445379894;
f:= (x) -> 0.9/abs(x-0.4)^(1/3)+0.1/abs(x-0.6)^(1/2);
U1 := unapply(-exp(-x)*(evalf(Int(f(t)*exp(t), t = 0 .. x))+G1)/2-exp(x)*(evalf(Int(f(t)*exp(-t), t = 0 .. x))+G1)/2, x);
U:= unapply(-exp(x)/2*(evalf(Int(f(t)*exp(-t),t=0..x))+G1)+exp(-x)/2*(evalf(Int(f(t)*exp(t),t=0..x))+G1), x);

Next, I calculate the integral in numerical form:

evalf(Int(U1(x)^2+U(x)^2-2*f(x)*U(x), x=0..1, digits=4, method = _Gquad));

If I specify digits=4, Maple return the answer -0.4291

If I use digits=5 or larger, Maple return someting like this

Is it possible to increase precision of calculation?


 

 

Hey guyz, I am in trouble with calculation attached integral. it is a simple function but a bit long. I can't solve it with maple, Do U have any idea?

 

 

intg.mw

 

 

Hi I try this integral:

m2 := int(exp(-(1/2)*z^2)*((exp(B*J*sqrt(q)*z))^2-1)/(sqrt(Pi)*sqrt(2)*((exp(B*J*sqrt(q)*z))^2+1)), z = -infinity .. infinity)

But not resolve.

How can i do?

Regards.

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

i could have sworn that when itegrating a gaussian maple will write it in terms of the erf functions... but i end up with:

gg:=A * exp( - ( (t - t0) / (tau) )^2 );
val1:=int(gg, t=-x0..x1) assuming t0::real, tau::real, x0<x1, t0>x0, t0<x1, x0::real, x1::real;  #or with no assumptions

 

the results is just gg unchanged... Doing:

convert(val1, erf)

does not help. I can set t0 (or transform it away), and it works, but I was hoping maple would not require this. 

Any thoughts how to help maple with this?

Mathematiaca can read my mind without issues:

 

Good evening sir.

 

I request your valuable support with regard to the above cited query.

 

 

With thanks & regards.

 

Mr.M.Anand

Associate Professor in Mathematics

Hi,
   I just finished a math quiz. I needed to find the length of the curve and area of the function, r=3*cos(theta)-2*sin(theta) bounded between 0<=Pi<=2*Pi.
   On the quiz I used Area=int(1/2*(r^2)) dtheta. For the length of the curve I used L=int(sqrt(r^2 + r'(theta)) dtheta.

How do you plug this into Maple and get an answer?
I came up with 20.42.... sq units for the area and 22.65.... for the length of the curve.

Thank you,
Jay.

I have 

dZ(x)=−xdlog(z(x))

where d is the exterior derivative. I would like to recover the function Z(x) by integrating both sides of the equation. How would I compute this in Maple?

 Dear All ! 

I really need to solve this problem as soon as possible, As you know the downside equation is not exact, but I can not find its integration factor, blease help me !

                                                                 ∫{ ( ωx + σy ) d x + (ωy −σx)dy}=0

 Regards ,

 

 

so I'm trying this:

restart;

sigma := 0.143e-18;

l_0 := 1.87;

l0 := 1.87;

roll := rand(0 .. 25.0);

f_gauss := proc (x) options operator, arrow; exp(-(1/2)*x^2/`&sigma;_x`^2)/sqrt(2*Pi*`&sigma;_x`^2) end proc;

f_norm := proc (dx) options operator, arrow; int(f_gauss(x), x = -(1/2)*dx .. (1/2)*dx) end proc;

sol_gauss := proc (mix) options operator, arrow; evalf(eval(-ln((int(f_gauss(x)*exp(-2*sigma*N2O*sqrt((1/4)*l_0^2-x^2)), x = -(1/2)*dx .. (1/2)*dx))/f_norm(dx))/(sigma*N2O), [N2O = 0.25e20*mix/100])) end proc;

for ii to 10 do

a := roll();

eval(sol_gauss(a), [dx = l_0, `&sigma;_x` = l0])

end do

After several attempts on this question,

Int(x*sqrt(2*x^4+3),x) with substitution u = sqrt(2)*x^2,

I don't seem to find the solution. Can you guys help me?

1 2 3 4 5 6 7 Last Page 1 of 14