Use simulation to approximate the integral

e^-(x+y)dydx, y from 0 to x, x from 0 to infinity

Compare your estimate with the exact answer if known. (

b) Estimate the area of the triangle T whose vertices are (0, 2), (2,6) and (5,0), by computing 500 i=1 I((Ui,Vi) T)/500, where (Ui, Vi), 1 500, are appropriate iid Uniform random variables.

Please write code in R.

1(a). Use simulation to approximate the integral 1 Compare your estimate with the exact answer if known. (b) Estimate the area of the triangle T whose vertices are (0, 2), (2,6) and (5,0), by computing 2509 I((U;,V;) E T)/500, where (Ui, V) 1 sis 500, are appropriate iid Uniform random variables