Question 460395
{{{(1/pi)*int(1/(1+x^2), dx, A) = ( 1/pi)*int(1/(1+x^2), dx, -infinity, infinity) = (1/pi)*(tan^-1(x))[-infinity]^infinity = (1/pi)*(pi/2-(-pi/2)) = (1/pi)*pi = 1}}}


{{{int(e^(-x), dx, 0, infinity) = (-e^(-x))[0]^infinity = 0-(-1) = 1}}}

There's a bit of a problem in the third question.  You have defined the set {{{A[k]}}} but have not defined the function OVER THAT SET.  The density function has to be dependent also on k OVER THAT SET for the questions to be answered.