Items tagged with integral

how to find the integration of z(x) form 0 to x with the given condition...
 

diff(z(x), x) = x*Typesetting:-delayDotProduct(b, 1+3*y(x))/(a^2*(1-(x/a)^2));

diff(z(x), x) = x*(b.(1+3*y(x)))/(a^2*(1-x^2/a^2))

(1)

`%%where%`, y(x) = b*((1-(x/a)^2)^(1/2)-(1-(R/a)^2)^(1/2))/(3*(1-(R/a)^2)^(1/2)-(1-(x/a)^2)^(1/2));

`%%where%`, y(x) = b*((1-x^2/a^2)^(1/2)-(1-R^2/a^2)^(1/2))/(3*(1-R^2/a^2)^(1/2)-(1-x^2/a^2)^(1/2))

(2)

with*condition; -1; z(R) = ln(1-(R/a)^2)

z(R) = ln(1-R^2/a^2)

(3)

``


 

Download integration.mw

How get answer of this integral

int(1/u.t.exp(-t/u), t = 0 .. infinity)

i want to have plot int.  but i get error 

"Error, (in type/EvalfableProp) too many levels of recursion"

how can i draw this plot

please help me . thank you

There seems to be a bug in determining the folowing integral analytically:

integrate(-(3/2*(exp(-(1/4)*x)*x-sqrt(Pi)*erf((1/2)*sqrt(x))*sqrt(x)))/(sqrt(x)*sqrt(Pi)*erf((1/2)*sqrt(x))), x = 0..1)

Maple gives as a result

3/2

However, numerically integrating it

integrate(-(3/2*(exp(-(1/4)*x)*x-sqrt(Pi)*erf((1/2)*sqrt(x))*sqrt(x)))/(sqrt(x)*sqrt(Pi)*erf((1/2)*sqrt(x))), x=0..1,numeric)

gives

0.1195461293

In fact, integrating it from a to b,

integrate(-(3/2*(exp(-(1/4)*x)*x-sqrt(Pi)*erf((1/2)*sqrt(x))*sqrt(x)))/(sqrt(x)*sqrt(Pi)*erf((1/2)*sqrt(x))), x=a..b)

gives

-3/2 a + 3/2 b

suggesting that Maple thinks the integrand is just 3/2. If one plots it, then it becomes obvious that this is not the case.

I dont understand how to approach this question, can anyone explain what it means by bessel and myJ?? Ive tried but i cant get the integral to work with the dy?

 

I  encountered a non-integrable integral in the process of solving the following process, . How to achieve its numerical solution? Such as in a looping   code:

#######
pa[i] := pa[i-1]-(Int(subs(t = tau, Lpa[i-1]+Na1[i-1]-Na2[i-1]), tau = 0 .. t)); 

pw[i] := pw[i-1]-(Int(subs(t = tau, Lpw[i-1]+Nw1[i-1]-Nw2[i-1]), tau = 0 .. t)); u[i] := u[i-1]-(Int(subs(t = tau, Lu[i-1]+Nu1[i-1]+Nu2[i-1]), tau = 0 .. t));

######
Detailed code see annexBC2.mw

Correct computatiton for

for reasonable expressions f(x,y), g(x,y) would be very useful in double integrals.

For the moment this is not possible. Too many bugs:

int(Heaviside(1-x^2-y^2), x=-infinity..infinity, y=-infinity..infinity); #should be Pi
                           undefined
int(Heaviside(1-x^2-y^2), x=-1..1, y=-1..1); #should be Pi
                               0
int(Heaviside(y-x^2), x=-1..1, y=-1..1); #should be 4/3
                               -2

int(Heaviside(y-x^2), y=-1..1, x=-1..1); #This one is OK!
                              4/3

 

 

 

 

Hi all,

 how to calculate this integral:

int(sqrt(a^2+cos(x)),x=0..Pi);

 

plz code and sole that this integral!!!!!!!!!!

!!!

How to evaluate a Stieltjes integral ?  I'm not asking for the definition of the Stieltjes integral, I want to know how I can get maple to evaluate one.

Hi all,

I am trying to plot in semilog scale a function involving products of exponential integrals and complex exponentials. For small and moderate values of the argument, the plot is well shown. However, for larger values the plot shows strong fluctuations. I was wondering how one can deal with such a problem. Any help is highly appreciated.

Please refer to the attached script for the functio of interest.

Thanks
F

 

Question.mw

 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 ,

 

 

Hi!

 

Suppose, we need to compute this integral:

int(sqrt(exp(2*I*t)-1),t) from t=0 to t=Pi

If we write this as definite integral, we get right answer: 2*sqrt(2)-(1/2)*ln(17+12*sqrt(2))

But in case of indefinite integral (computing antiderivative) one gets I*arctan(sqrt(exp(2*I*t)-1))-I*sqrt(exp(2*I*t)-1). Substitution t=Pi and t=0 both lead to 0, so we can't transform antiderivative to definite integral. What is the reason?

Hi guys,

 

I am trying to solve a Fredholm equation of the second kind using Maple. An analytical expression cannot be in principle found. I was wondering whether Maple does numerical evaluation of such integral equations. Please see the equation in attach. Any help is highly appreciated.

Thanks

F

 

Question.mw

 

Hello all. Is there any solution for the indefinite integralBadIntegral.mw

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int((B*alpha[1]+(1/8)*`Νu`)*HeunT((1/16)*alpha[1]*(8*B*alpha[1]+`Νu`)*3^(2/3)*(2*alpha[2]+1)^2/(alpha[2]*(alpha[1]*alpha[2]*(8*B*alpha[1]+`Νu`))^(1/3)), 0, (1/2)*alpha[1]*(8*B*alpha[1]+`Νu`)*3^(1/3)/(alpha[1]*alpha[2]*(8*B*alpha[1]+`Νu`))^(2/3), (1/3)*3^(2/3)*(alpha[1]*alpha[2]*(8*B*alpha[1]+`Νu`))^(1/6)*y), y)

int((B*alpha[1]+(1/8)*`Νu`)*HeunT((1/16)*alpha[1]*(8*B*alpha[1]+`Νu`)*3^(2/3)*(2*alpha[2]+1)^2/(alpha[2]*(alpha[1]*alpha[2]*(8*B*alpha[1]+`Νu`))^(1/3)), 0, (1/2)*alpha[1]*(8*B*alpha[1]+`Νu`)*3^(1/3)/(alpha[1]*alpha[2]*(8*B*alpha[1]+`Νu`))^(2/3), (1/3)*3^(2/3)*(alpha[1]*alpha[2]*(8*B*alpha[1]+`Νu`))^(1/6)*y), y)

(1)

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Download BadIntegral.mw

?

 

Thanks

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