Integrate the kernel of the χ density r d−1 exp{−r 2 /2} on (0,∞) for various values of d. (a) Find a truncation point. How does it depend on d? (b) How many points are required using Simpson’s rule...

Integrate the kernel of the χ density r d−1 exp{−r 2 /2} on (0,∞) for various values of d. (a) Find a truncation point. How does it depend on d? (b) How many points are required using Simpson’s rule to get the relative error below 10−4?

Integrate the function f(x) = 1/(1+ x2) on (−1,1) using the Siegel–O’Brien randomized quadrature method.