How could i solve this equation numerically if the Phi value is dependent on Theta?

[kmohamed]

have a problem in solving a numerical double integration, two variables dependent on each other, the boundary for one of them is known, but the other is not.

tried to sole it in mathcad but i think that there is an error in inputs, or how to put it in mathcad in the right manner

[LucMeekes]

Did you just want these:

and

Or also values in between:

with:

plots as:

Sucess!

Luc

Careful, attached file is in Prime 4, you need prime 4 to read it!

[kmohamed]

thanks for your kindly reply

but i need a single value depend on theta and phi

[Fred_Kohlhepp]

I think the attached file does what you want.

Your integral evaluates to a single value.

File is Prime 3.0

[kmohamed]

thanks Mr.Fred

but why you replace phi in the equation by s, the value of this equation is unit-less, my target is not to calculate phi, but a unit-less value depend on both theta and phi, so is that possible?

[Fred_Kohlhepp]

"s" is a variable of integration.

Attached file has a bit of explanation, I hope it helps.

[kmohamed]

yes i get it,

Does the output unit is in degree ( or have a unit), because in my status the output is unitless?

it's divided by 2*Pi

[Fred_Kohlhepp]

The default "unit" for angle in Mathcad is the radian.  Since a radian is a ratio (length / length) it displays no units.  You have a lot of unitless constants in your expression.  If these are supposed to have units (length?) that may affect your results.  You may choose to give an angle the unit degree, Mathcad will automatically convert from radians if you insert the unit: