I don't understand why I solve the integration in two different ways and get two different answers!!(adsbygoogle = window.adsbygoogle || []).push({});

To find:

[tex]\int_0^{\pi} P_1^1(cos \theta) sin \theta d \theta [/tex]

1) Solve in [itex] \theta[/itex]

[tex] P_1(cos \theta) = cos \theta \;\Rightarrow \; P_1^1(cos \theta)= -sin \theta [/tex]

[tex]\int_0^{\pi} P_1^1(cos \theta) sin \theta d \theta = -\int_0^{\pi}sin^2 \theta d \theta = -\frac{\pi}{2}[/tex]

2) Let [tex]s=cos \theta \;\Rightarrow \; d\theta = \frac{ds}{-sin \theta} [/tex]

[tex]\int_0^{\pi} P_1^1(cos \theta) sin \theta d \theta = -\int _1^{-1} P_1^1(s)ds[/tex]

[tex]P_1(s)=s \;\Rightarrow P_1^1(s)=1[/tex]

[tex]\int_0^{\pi} P_1^1(cos \theta) sin \theta d \theta = -\int _1^{-1} P_1^1(s)ds = -s|_1^{-1} = 2[/tex]

You see the two method yield two answers!!! I know it should yield the same answer, the book show how to solve the problems in 2) form. Please tell me what did I do wrong.

thanks

Alan

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Please help in integration of Associate Legendre function

**Physics Forums | Science Articles, Homework Help, Discussion**