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Lenin10-Marble
10-Marble
Dec 5, 2025 3:34 PM UTC
Solved

Help on solving integration

Dear community,

 

Can someone help me solve the integral of the following equation in Mathcad 7.0.0.0? Only J(x) and tau(x) vary with x, and the rest are constants.

Lenin_1-1764948358988.png

Thanks in advance

Werner_E
Werner_EAnswer
25-Diamond I
Dec 5, 2025 4:14 PM UTC

If only J and tau depend on the variable x we can assume that the left hand side is constant as well.

Werner_E_0-1764950656694.png

or

Werner_E_1-1764950668989.png

 

I notice that

1) you have two functions to solve for, but only one equation !!??

2) If x=0 the integral is zero. What is J(0) and tau(0) supposed to be?

As I assume that the constant on the right hand side should not be not zero, this means either J(0)->infinity and/or tau(0)->0

 

So I would say that one equation is not enough information and once you fix that, you may search the forum for "integral equation"
Posts - PTC Community

and see if you can find something useful, as Prime has no facility out of the box to solve an integral equation.

 

You could differentiate your equation

Werner_E_0-1764952639869.png

with respect to x and with a little help from Prime's symbolics

Werner_E_1-1764952672907.png

Werner_E_2-1764952678894.png

you can write

Werner_E_3-1764952706370.png

You now need a second equation and then you could try to solve that system in a solve block with "odesolve".

I have no idea if this would work OK but it may be worth a try...

 

 

 

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2 replies

Werner_E
Werner_E25-Diamond IAnswer
25-Diamond I
Dec 5, 2025 4:14 PM UTC

If only J and tau depend on the variable x we can assume that the left hand side is constant as well.

Werner_E_0-1764950656694.png

or

Werner_E_1-1764950668989.png

 

I notice that

1) you have two functions to solve for, but only one equation !!??

2) If x=0 the integral is zero. What is J(0) and tau(0) supposed to be?

As I assume that the constant on the right hand side should not be not zero, this means either J(0)->infinity and/or tau(0)->0

 

So I would say that one equation is not enough information and once you fix that, you may search the forum for "integral equation"
Posts - PTC Community

and see if you can find something useful, as Prime has no facility out of the box to solve an integral equation.

 

You could differentiate your equation

Werner_E_0-1764952639869.png

with respect to x and with a little help from Prime's symbolics

Werner_E_1-1764952672907.png

Werner_E_2-1764952678894.png

you can write

Werner_E_3-1764952706370.png

You now need a second equation and then you could try to solve that system in a solve block with "odesolve".

I have no idea if this would work OK but it may be worth a try...

 

 

 

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    terryhendicott
    terryhendicott21-Topaz II
    21-Topaz II
    Dec 6, 2025 5:16 AM UTC

    Hi,

    Took a different approach.  J(x) is a function of x, but from the earlier equations tau(E(x)) is a function of E at x not just x

    Means the following is possible?

    Capture.JPG

    Not sure if this is correct but it is possible!

    Cheers

    Terry

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