Problem 179. Monte-Carlo integration

Solution 188645

Submitted on 9 Jan 2013 by Tomasz

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Test	Status	Code Input and Output
1	Pass	%% 1d integral: integrate x^2 from 0 to 1 fun = @(x) x^2; assert(abs((dquad(1,fun) - 1/3)*3)<0.01) ans = 0.3332
2	Pass	%% 2d integral from the example fun = @(x) x(1)x(2); assert(abs((dquad(2,fun) - 0.25)4)<0.01) ans = 0.2504
3	Pass	%% constant in most dimensions fun = @(x) 1+sin(x(1)); assert(abs((dquad(50,fun) - 1.45969769)/1.45969769)<0.01) ans = 1.4593
4	Pass	%% volume of d-dimensional 2^d box with a spherical hole, d between 5 and 10 d = randi([5 10],1) r = rand0.8 fun = @(x) 2^d(norm(x)>r); dball = exp(d/2log(pi)+dlog(r)-gammaln(d/2+1)); assert(abs((dquad(d,fun) - 2^d+dball)/(2^d-dball))<0.01) d = 7 r = 0.7585 ans = 127.2768

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