format long%% x^2+y^2 integrated from -1 to 1 in x and -1 to 1 in y = 8/3%[bx,by,w]=grule2d(2,2);vol1=gquad2d('gxy',-1,1,-1,1,bx,by,w)% orvol1a=quad2dg('gxy',-1,1,-1,1)% orvol2=gquad2d('gxy',-1,1,-1,1,2,2)% ornvol1= gquadnd('hx',[-1;-1],[1;1],[2;2])% ornvol1a=quadndg('hx',[-1;-1],[1;1])correct_ans=8/3%% x^2+y^2 integrated from 0 to 2 in x and 0 to 2 in y = 32/3%vol3=gquad2d('gxy',0,2,0,2,bx,by,w)% orvol3a=quad2dg('gxy',0,2,0,2)% orvol4=gquad2d('gxy',0,2,0,2,2,2)% ornvol2 = gquadnd('hx',[0;0],[2;2],[2;2])% ornvol2a = quadndg('hx',[0;0],[2;2])correct_ans=32/3%% x^2+y^2 integrated from 0 to 3 in x and 0 to 3 in y = 54%vol5=gquad2d('gxy',0,3,0,3,bx,by,w)% orvol6=gquad2d('gxy',0,3,0,3,2,2)% or% nvol3 = gquadnd('hx',[0;0],[3;3],[2;2])correct_ans=54%% x^2+y^2 integrated from 0 to 3 in x and 0 to 3 in y = 54% with the general area of intergration (functional limits in x)%[bx2,wx,by2,wy]=grule2dgen(2,2);vol7=gquad2dgen('gxy','gliml','glimh',0,3,bx2,wx,by2,wy)% orvol8=gquad2dgen('gxy','gliml','glimh',0,3,2,2)% orvol8a=quad2dggen('gxy','gliml','glimh',0,3)correct_ans=54%% x^2+y^2 integrated from 0 to y in x and 0 to 2 in y = 16/3%vol9=gquad2dgen('gxy','gliml','glimh2',0,2,bx2,wx,by2,wy)% orvol10=gquad2dgen('gxy','gliml','glimh2',0,2,2,2)correct_ans=16/3%% 1 integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x % and -2 to 2 in y = 4*pi -- area of circle with radius 2 or (pi r^2)%vol11=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,bx2,wx,by2,wy)% orvol12=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,2,2)correct_ans=4*pi%         ---  same problem better quadratue (more points)% 1 integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x % and -2 to 2 in y = 4*pi -- area of circle with radius 2 or (pi r^2)%[bx3,wx3,by3,wy3]=grule2dgen(5,5);vol13=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,bx2,wx,by2,wy)% orvol14=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,5,5)correct_ans=4*pi%% sqrt(x^2+y^2) integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x % and -2 to 2 in y = 16*pi/3%% Need higher order quadrature[bx3,wx3,by3,wy3]=grule2dgen(10,10);vol15=gquad2dgen('gxy2','lcrcl','lcrcu',-2,2,bx3,wx3,by3,wy3)% orvol16=gquad2dgen('gxy2','lcrcl','lcrcu',-2,2,10,10)correct_ans=16*pi/3%% 1/sqrt(1-x^2) integrated from -1 to 1 in x  = pi%% Use Gauss-Chebyshev quadrature[bpc,wfc]=crule(2);area1=gquad('gxy1',-1,1,1,bpc,wfc)%orarea1a=quadc('gxy1',-1,1)correct_ans=pi%% x^2/sqrt(1-x^2) integrated from -1 to 1 in x  = pi/2%% Use Gauss-Chebyshev quadraturearea2=gquad('xsquar',-1,1,1,bpc,wfc)area2a=quadc('xsquar',-1,1)correct_ans=pi/2