Let $\rho ( r , \theta ) = \frac { \theta } { \pi ^ { 2 } }$ be a joint probability distribution function on the unit disk. What is the probability of an event occurring in the region bounded by the spiral $r = \frac { \theta } { 4 } , 0 \leq \theta \leq \pi$ and the x-axis?

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The Answer of Let $\rho ( r , \theta ) = \frac { \theta } { \pi ^ { 2 } }$ be a joint probability distribution function on the unit disk. What is the probability of an event occurring in the region bounded by the spiral $r = \frac { \theta } { 4 } , 0 \leq \theta \leq \pi$ and the x-axis?

Let ρ(r,θ)=θπ2\rho ( r , \theta ) = \frac { \theta } { \pi ^ { 2 } }ρ(r,θ)=π2θ​

Let $\rho ( r , \theta ) = \frac { \theta } { \pi ^ { 2 } }$