Solid Angle Rutherford Scattering

[Purple Baron]

Homework Statement

derive an equation for the solid angle for a Rutherford scattering detector given a detcor window area of $A$ and a distance to the detector of $D$ for some scattering angle $\phi$ given that $d\Omega =2\pi sin\phi d\phi$

Homework Equations

$d\Omega =2\pi sin\phi d\phi$
$A=Dd\phi$

The Attempt at a Solution

integrating $d\Omega =2\pi sin\phi d\phi$ to get solid angle gives $\Omega =\frac{2\pi A}{D}\int sin\phi d\phi$ howver this gives a negative value due to the integral of sine and shouldn't soild angle be positive? Is this correct or am i missing a step? Thank You

 

[BvU]

You sure this gives a negative value ? Can you show how you get it ? Bounds, primitive ?

 

[haruspex]

A=Ddϕ

That's dimensionally incorrect. You have an area on the left and a distance on the right. And the dϕ looks wrong.
Shouldn't it be $A = D^2d\Omega$?
As BvU posted, your problem with the negative sign will resolve itself when you put in the bounds on ϕ.