- #1

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Nevermind, I seem to have figured it out

show that:

[tex]\int \frac{dN}{N} = \int_{0}^{\theta_max} \frac{dcos \theta}{2} \frac{1 + \frac{v^2}{v_0^2} cos(2 \theta ) }{ \sqrt{ 1 - \frac{v^2 sin^2 \theta}{v_0^2} } } [/tex]

I'm having a lot of difficulty doing this...

Note that [tex]sin(\theta_{max} ) = \frac{v_0}{v}[/tex]

so after a bunch of algebra I get:

[tex]\int \frac{dN}{N} = cot(\theta_{max} ) \int_{0}^{\theta_{max} } \frac{2y^2 - 1}{\sqrt{y^2 - 1} }[/tex]

I am fairly confident that is correct because I keep on getting it.

Unfortunately, I can't seem to integrate this at all.

## Homework Statement

show that:

[tex]\int \frac{dN}{N} = \int_{0}^{\theta_max} \frac{dcos \theta}{2} \frac{1 + \frac{v^2}{v_0^2} cos(2 \theta ) }{ \sqrt{ 1 - \frac{v^2 sin^2 \theta}{v_0^2} } } [/tex]

## Homework Equations

## The Attempt at a Solution

I'm having a lot of difficulty doing this...

Note that [tex]sin(\theta_{max} ) = \frac{v_0}{v}[/tex]

so after a bunch of algebra I get:

[tex]\int \frac{dN}{N} = cot(\theta_{max} ) \int_{0}^{\theta_{max} } \frac{2y^2 - 1}{\sqrt{y^2 - 1} }[/tex]

I am fairly confident that is correct because I keep on getting it.

Unfortunately, I can't seem to integrate this at all.

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