Consider the integral

=0/4/23/4x2y2sin(x+y)ln(x+y)dydx

Construct a stratified-sampling plan to estimate with stratification on the variable x using the combinations ofr=24 andr=28 strata and220/r samples per stratum, respectively. In each case partition the interval[0,/4] into r equal-length subintervals. Use the uniform density to draw samples in each x-interval and th uniform distribution on[/2,3/4] to draw samples for Y. In each of the two cases, report the point estimate of along with its standard and relative errors, the variance ratio, and the running time.

Feel free to use your programming language.