Items tagged with integral

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I am not able to understand why Maple fails to compute and display the integrals for Eqn (1) and Eqn (8). I have a integral table to cross-verify the integrals for each of these in here

 

Also, another integral I am trying to calculate in MWE2 (attached file) in which the integral computed doesn't make any sense.

MWE-2.mw

 

int(sqrt(x^3.(ax+b)), x)

int((x^3.(ax+b))^(1/2), x)

(1)

2+2

4

(2)

int(7*x^3+3*x^2+5*x, x)

(7/4)*x^4+x^3+(5/2)*x^2

(3)

int(1, x)

x

(4)

int(1/(x^2+1), x)

arctan(x)

(5)

int(1/(ax^2+bx+c), x)

x/(ax^2+bx+c)

(6)

int(x^n, x)

x^(n+1)/(n+1)

(7)

int(sqrt(x(ax+b)), x)

int(x(ax+b)^(1/2), x)

(8)

``


 

Download MWE-1.mw

i solve a dynamic problem but i get wrong answer. F (load) after 0.02 then to zero but d (displaciment) not go to zero 

1.mw  

New_Microsoft_Excel_Worksheet1.xlsx

How to plot an Elliptical Function of Third kind complete or incomplete, eg. EllipticPi(n,k) if n and k are not constants?

as The function I wish to plot and explore contains Elliptical Function of Third kind complete and incomplete with complicated form of n and k.

Please reply asap.

Regards

how would you interpret the solutions to this:

>int(sin(y/2)^2/(x*(x-y)*y^2), x=omega__ir*t..omega__c*t) assuming t::positive, omega__ir::positive, omega__c::positive, omega__c>omega__ir;
 

which leads to the expression shown in the screen shot. In particular, I'm interested in the condition for the solution to be "undefined"

thanks.

Hi, friends

I need to calculate the double integral over a non-rectangular domain.

Say, the domain is the triangle (in red)

When I enter

int(int((x^2+y^2)*`if`((y-x-1/2 <= 0) and (y+2*x-2<=0) and (y+x/2-1/2>=0), 1, 0), x=0..1, numeric = true), y=0..1, numeric = true);

or 

int(int((x^2+y^2)*eval(`if`((y-x-1/2 <= 0) and (y+2*x-2<=0) and (y+x/2-1/2>=0), 1, 0)), x=0..1, numeric = true), y=0..1, numeric = true);

an error occur (Error, (in int) cannot determine if this expression is true or false: y-x <= 1/2 and y+2*x <= 2 and 0 <= y+(1/2)*x-1/2)

For me, it is desirable to write boundary conditions in the int operator itself, not as a separate expession.

 

If I just want to define an itegral and do not want maple to simplify it to a closed form, what should I do?

For example, I want define

s := int(exp(-x^2)*cos(2*x*y), x = 0 .. infinity).

Maple automatically simplify s to

(1/2)*sqrt(Pi)/exp(y^2)

But I want to keep s in integral form.

Hi,

I want to solve the integral with respect to Gamma function but I can not obtain it by maple. the lower limit "a" is very close to zero. Please direct me. Thank you

Integral.mw


 

 

 

 

int(exp(I*x(2-y)),[x=-infinity..infinity, y=0..2]);

how to calculate this integral? where I is imaginary part?

I am trying to evaluate the following double integral where hypergeom([x,1/2],[3/2],C) is gauss hypergeometric function 2f1. maple gives back it unevaluated. I doubt it may be due to slow convergence of hypergeometric function. 
 

restart; x := (1/6)*Pi; evalf(int(evalf(int(cos(x)*hypergeom([x, 1/2], [3/2], sin(x)/(r*cos(x)+k-2*r*sin(x))^2)/(r*sin(x)^2+r*cos(x)+k)^4, k = 0 .. 10)), r = 1 .. 2))

Int(Int(.8660254040*hypergeom([.5000000000, .5235987758], [1.500000000], .5000000000/(-.1339745960*r+k)^2)/(1.116025404*r+k)^4, k = 0. .. 10.), r = 1. .. 2.)

(1)

``


 

Download DOUBLE_INT_2.mw

hello. how can i solve this integral. thank you

int(ln(x)^n,x)  just returns the integral

Mathematica gives

What other interventions are required to get Maple to produce an answer?

 

I just quickly checked Nasser Abassi 12000.org to see if he's updated it for Maple 2017.  In some areas he has.  I thought I would check one of the integrals that failed for Maple in his tests.  In the Computer Algegbra independent integration tests Maple failed to solve 11.68% of the 3407 integrals in his test while Mathematica only failed 0.88%.  For Maple that seemed quite high, so it is perhaps his method of solving for Maple and perhaps he's more adept with Mathematica. 

Here is one of the failed integrals and the single line code he used to solve it.

int((5*x^2+3*(x+exp(x))^(1/3)+exp(x)*(2*x^2+3*x))/x/(x+exp(x))^(1/3),x) # of course because it failed it just spits back the integral.

Can maple solve it?

The answer is supposed to be

 

I need to calculate the following complex integral:

oint_C { [(z^4exp(2z)+1)/(z+i)^3] - [(z^3+z)/{(z-2i)(z-5)}] + 8*Pi*exp } dz,

 

Where C is the circumference |z-1| = sqrt(11/2), positively oriented.

 

Someone can help me, I already researched but I can not integrate.

3.mw

There are 2 questions actually. The first as the title says is about taking the integral. I have 2 functions that were found numerically from the system of differential equations (see the file), and I need to take the integral of the expression that includes both of them. Maple gives me something like Int () = Int (), so it doesn't solve anything. Why can it be?

The second question is about varying the boundary conditions. If, for example, I have the system with the condition like R(x_0)=R_0, can I get the plot  of R(x,R_0)? In my case I need to vary conditions on R and mu (R(0)=R_0 and mu(0)=mu_0) and then get the plot of the integral in relation to R_0 and mu_0. Is it even possible?

Can someone answer why i get Float(undefined) while computing integral

Here is my example

NULL

restart

with(plots):

NULL

alpha0 := .3;

.3

(1)

R := .1;

.1

(2)

sigma := 636;

636

(3)

Kfc := 101;

101

(4)

Ksc := 9;

9

(5)

E := 2*10^5;

200000

(6)

`&delta;th` := 2*10^(-7);

1/5000000

(7)

`&delta;c` := 0.8e-1*10^(-3);

0.8000000000e-4

(8)

p := 400;

400

(9)

`l&delta;z` := 12.1*10^(-3);

0.1210000000e-1

(10)

lKz := 20.3*10^(-3);

0.2030000000e-1

(11)

eta := 10^(-5);

1/100000

(12)

l0 := 0;

0

(13)

xi := p/sigma;

100/159

(14)

KImax := evalf(p*sqrt(Pi*l));

708.9815404*l^(1/2)

(15)

``

`N&delta;` := evalf(E*sigma*(int((-xi^2+1)*(-KImax^2+Kfc^2)/((KImax^2-Ksc^2)*((-R^4+1)*(KImax^2+Ksc^2)+eta*E*sigma)), l = l0 .. `l&delta;z`))/alpha0);

Float(undefined)

(16)

``

NULL

NULL

NULL

NULL

NULL

``

``

``

``

``

NULL

NULL


 

Download N.mw

Thanks in advance

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