I'm trying to calculate an individual probability $P(\hat{a})$ from a joint probability $P(\hat{a},\hat{b})$ in a physics application, where $\hat{a},\hat{b}$ are unit vectors.
I need to evaluate the following integral:
$P(\hat{a})=\int P(\hat{a},\hat{b}) d\hat{b}$
The value of the joint probability is $P(\hat{a},\hat{b})=\frac{1}{4}[1+\hat{a}\cdot\hat{b}]=\frac{1}{4}[1+\cos\theta_{ab}]$.
I'm not really sure how to begin dealing with this integral. Any pointers would be greatly appreciated!
Thanks in advance.