Question

Find the constant c so that a random variable X is defined assigning any interval [a,b] probability c/π⋅∫ba (1/x^2+1) dx

Answer 1

I think is the arctan over something

Answer 2

we want to find c such that the function above is a density function?

Answer 3

\[\text{ and yes } \int\limits \frac{1}{x^2+1} dx=\arctan(x)+K \\ \text{ where } K \text{ is the constant of integration } \\ \text{ and we don't need } K \text{ since you have } \int_a^b \frac{1}{x^2+1}dx=\arctan(x)|_a^b\]
and you can multiply both sides by your constant multiple above the c/pi thing

Answer 4

is 1